This is a partial answer and a collation mostly from Wikipedia articles.
It would appear the the sloop Neva passed through Sitka in 1810 to deliver a salt cargo under the command of Ludwig von Hagemeister. The Neva was travelling from Hawaii. The Neva would later attempt to return to Sitka in 1812 but hit a rock and sank with the loss of 32 of the 75 onboard. It was carrying furs and guns from Okhotsk. It is possible that in between its passage in 1810 and its sinking in 1812 it came to Sitka again.
Again in 1810 a ship visited Sitka to drop off Russians rescued from an ill fated expedition that was to explore the Oregon coast. The American merchantman Lydia arrived on June 9th.
Also during 1810 there appears to have been a visit by another American ship which could have been the Lydia. The purpose of this visit being trade on behalf of John Jacob Astor. The ship then purportedly went to trade furs at Guangzhou.
It would seem that visits from merchantmen was relatively common since Sitka was the capital of the Russian-American Company that exported furs.