First, let's correct some assumptions in the questions...
Why did the US send P-400s instead of more F4F Wildcats or P-40 Warhawks?
From what I can tell, they did send more Wildcats. In the first critical weeks of operation it was F4F Wildcats of Navy and Marine squadrons VMF-212, VMF-223, VMF-224, VF-5 defending Henderson field.
There was also a single squadron of Army P-400s, the 67th Fighter Squadron. This was the only Army fighter squadron at Henderson field. The 67th had what the Army had available when they shipped out from the US: P-400s.
(AFAIK no P-40s were sent to Guadalcanal. The mention of nine P-40s in the WW2 DB article is a typo, it is nine P-400s.)
Was sending P-400s a blunder compared to sending other planes?
No, there were critical shortages of US Army aircraft in the South Pacific and they sent what was available. After the P-400s gave up trying to be interceptors, they were very useful as ground attack aircraft and freed up the Wildcats for other duties.
...since stockpiles at Henderson Field were the main point against sending thousands of airplanes at Henderson Field
While better supply certainly would have helped, all the supplies in the world wouldn't Henderson operate thousands of aircraft.
"RXI" airfield, later Henderson Field, under construction by the Japanese in July 1942
Henderson was a tiny forward airstrip hacked out of the jungle on swampy terrain with captured Japanese equipment. In early September a second strip, really just flattened sod, was built for the lighter fighter aircraft. Bombers used the more developed original strip.
Both strips were continuously attacked by bombers, artillery, and naval gunfire. The best defense for all aircraft was to get airborne as fast as possible during these attacks. The airstrips could only support so many takeoffs at a time. Crowding the airfield with more aircraft would turn more aircraft into ground targets.
To understand why the USAAF was using inferior export aircraft, look at this graph.
We think of the US as being this industrial juggernaut with endless supplies of ships and tanks and planes. That's true in 1943-1945. But Guadalcanal was 1942, the first year of the war for the US.
Prior to the war the US military was tiny and grossly underfunded, spending about 1-2% of its GDP on their military. Most of that went to the Navy. In 1941 that went up to about 5% and then skyrocketed from there. It wouldn't be until 1942 and 1943 when things really got rolling.
All this new equipment has to be developed, tested, produced, packaged up, transported, loaded onto ships, ferried thousands of miles across open ocean, unloaded, unpacked, reassembled, tested, and sent to the front line. Often under terrible conditions.
In 1942 while the US is rebuilding their military and making up for their extensive losses in the Pacific, they're also arming Britain, Australia, Canada, the Soviets, the Chinese, etc... and were gearing up to invade North Africa, and were preparing their first major ground offensive in the Pacific: Guadalcanal.
Finally, while the US Navy made the Pacific their priority, Europe was the strategic priority for the US Army and the Allied war effort.
The supply situation in the South Pacific was so dire that in 1942 the US Army Air Forces and Royal Australian Air Force had to pool their resources to keep their P-40 equipped units flying.
The situation on Guadalcanal
Fast forward to 7 August 1942. The Japanese are constructing an airfield on Guadalcanal which would threaten supply routes to Australia. In a surprise attack, the 1st Marine Division has takes the partially constructed airfield. Later that night the US Navy is badly beaten at the Savo Island withdraws their transports before they finish unloading, and carrier air cover. Fortunately the Japanese are surprised and their response is slow allowing the Marines to complete Henderson Field on 19 August (the exact dates are messed up because of the international date line) allowing 19 Marine Wildcats of VMF 223 to arrived from the Escort Carrier USS Long Island.
The next day the Japanese begin landing troops on Guadalcanal. Henderson Field needs reinforcement NOW!
USAAF 67th Fighter Squadron
The P-39 and P-40 were the US Army's brand new pursuit aircraft to replace obsolete aircraft such as the P-36. The USAAF had only ordered 60 P-39Cs in August 1939, and after seeing the war in Europe, decided they needed an improved P-39D. By Pearl Harbor about 600 P-39s had been built, but mostly for export Britain.
After Pearl Harbor the US Army needed to re-equip its squadrons NOW. So the Army nabbed 200 P-39s from the British order, called it the P-400, and designated them for units headed to the Pacific.
Into this dire supply situation enter the US Army Air Corps 67th Pursuit Squadron (later US Army Air Forces 67th Fighter Squadron). Prior to 1942 they were flying P-35 training aircraft. In January 1942 the 67th, with only half its complement of pilots, they were sent to the Pacific with 47 crates of an unknown type of aircraft. In March they landed in New Caledonia to find 45 untested and disassembled P-400s and 2 P-39Fs, sometimes missing parts, sometimes flawed parts, and with no replacements. They went about slowly assembling and getting to know these unknown-to-them aircraft and patrolling around New Caledonia.
As the Guadalcanal invasion is happening, the 67th is ordered to move to the Solomons. This is at the edge of their range, their first five P-400s arrive on August 22nd, but despite their attempts were unable to intercept the high flying Japanese bombers; that was left into Marine Wildcats. Nine more P-400s arrived on Aug 27th. On Aug 30th they went after what they thought were dive bombers which turned out to be Zeros and were left with just three serviceable P-400s.
After that they were no longer allowed to attempt intercepts. Instead, they turned to ground attack performing close air support and attacking Japanese supply ships with cannons and 500lb bombs. At the Battle of Edson's Ridge, three P-400s helped break up the final Japanese attack. The P-400s continued to be useful as ground and naval attack aircraft through the critical early months of the campaign.
A Brief History Of Wildcat Production
This sudden rearmament meant bringing brand new equipment into production. The US Navy had been flying biplanes until 1939 when they bet on their first monoplane, the Brewster Buffalo. They ordered 54 Wildcats in Aug 1939 to hedge their bets in case the Buffalo didn't work out (it did not work out). France ordered 81 in 1939, but France fell before they were delivered; they were given to the Royal Navy who began operating them in 1940 a year before the US Navy. More Wildcats were sent to Greece in spring 1941 to bolster their defense.
Official adoption of the Wildcat by the US Navy did not come until October 1941. By Pearl Harbor the US Navy Fighting Squadrons were still transitioning away from the F3F biplane. More Wildcats were lost at Pearl Harbor, Wake, and other Japanese attacks.
Guadalcanal was just 9 months later in August 1942. Meanwhile the US Navy needed Wildcats to...
- Replace losses from Dec/Jan Japanese attacks
- Seven fleet carriers worth of Fighting Squadrons to fill out (up to 27 per carrier)
- 20+ new escort carriers to equip (wildly variable numbers)
- Various island garrisons
- Training squadrons
- Replace combat and operational losses during 1942
You begin to see why they couldn't just send more Wildcats; Pearl Harbor caught the US Navy transitioning and just working up production. The Wildcat was brand new, top of the line, and in very high demand. The US had no comparable carrier fighter.
That said, they did sent Wildcats. Henderson Field was mostly defended by Wildcats from both Marine and Navy squadrons.