I have an old document, handwritten probably in the mid 19th century, which mentions 'Unalashka' as a place or area.

Is this an old name for Alaska?

In the Aleutian Islands, off the southwest coast of Alaska, there is an island and town on that island that are called Unalaska. "Unalashka" may very well be an older spelling variation of this island.

Yes, that would fit. You can see the full text in this post. I think it was probably written down as heard spoken. That would explain the intrusive 'h' as well as the other oddities.

I'm obliged t'ye, Sir.

And you are very welcome, Sir!