Would an AI package that forced the creature to find and use furniture make it sit down in a chair? If not, how could I get a skeleton to sit in a chair without making any new animations?

In short, just no to everything.

You would need a new animation, and that's just the half of it. Making the creature actually play the sitting animation correctly in the chair after it activated it is the real struggle.

I'd honestly look for an alternative scenario in your mod.

Also, I dont even know if creatures can use things like chiars etc.....