Will the BioCube skimmer that is rated for the 12 and 24g work ok in my 10 gallon nano, not a biocube? I'm also in the process of making a 2.5g refugium too, so if the skimmer is ok, will it be fine in the reguium as well?

I guess no one knows.

Yes, it will work. It is just an airstone driven skimmer. Thats all. It will work in the fuge or wherever. The only thing about those is that you need to replace the airstone regularly, maybe once a month is best( or whenever the bubbles become significantly reduced because of sludge buildup), but the stones are pretty cheap, especially if you buy online in bulk.

That being said, you will need an air pump as well if one is not included (I cant remember if it is)

if it will work on a 24 it will work on a 10 gallon