I'm also writing a naval story in the same time period, and I've amassed many different resource books. I know it's not a free source, but I have one book,
The Pirate's Primer ,that has a listing of many commands (easily upwards of 100). To me, it's an extremely useful resource for the time period, even though its main function is to help a writer flesh out their pirate characters so they say more than aargh. I actually find the pirate speak stuff the least useful.
But it has the exact types of commands you're looking for, stuff like 'wear ship', 'weather quarters', 'tacks and braces', 'turn the hands up', 'shake up the main', 'pipe to quarters', 'rouse away', 'keep her trimmed by the head', 'helm a-starboard', 'full and by', etc, etc. I don't know if it's allowed, but I could write a post with a bunch of commands in it and their explanations. The next step is to know what actually happens as the sailors carry out the order (which is really a far deeper rabbit hole than just knowing the commands).
Another great source is the actual
Textbook of Seamanship, that all midshipman were required to read during the age of sail. I know it's dated 1891, but it's basically the same book they'd read 100 years earlier. There are different ship commands mentioned throughout, but you'd need to read through the thing to find them all.
One thing to keep in mind too is that even in the Royal Navy, there really was no definitive set of commands (or uniforms, punishments, rigging, etc.) standardized at that period in time. So every ship and captain could be different. If your characters are on a private vessel, they'd have even more freedom to just issue whatever orders in whatever style they wanted.