Sparta always was a closed society, and the exact numbers of citizens (i.e. warriors) were an absolutely secret information all the time, no doubt.
After all, what do we know for sure? In the Battle of Platea there were 5000 spartiates, 5000 perioikoi, and 35000 helots. Also let's add that Plutarch in "Lycurgus" mentions 39000 shares in Laconia: 9000 spartiates families, and 30000 perioikoi.
Thus no one really doubts that there were several times more helots and perioikoi than spartiates. And the situation was only getting worse. So Brasidas even had to recruit helots-hoplites. Moreover, there is a point of view that only helots of Laconia were ever recruited. But the helots of Messenia - never. Probably even Spartans themselves never knew how many helots of Messenia are there.
So we don't know what percentage of population of Sparta were spartiates, but compared to the full population of Laconia and Messenia they were a negligible part, for sure. Those 15%, you've mentioned, may be reached only after later manumissions of neodamodes and such.