I've used it for years and don't find it drying at all.
As far as your question about whether it's safe or not, I've not been able to find anything that says it's not and isopropyl alcohol is made for use on the skin.
I know EWG doesn't like it so much but, in small amounts, I'm ok with it. I wouldn't bathe in it but, for me, a spritz under the pits is ok.
edited to add that alcohol is in everything from shampoo to lotion to mouthwash and toners. I feel pretty secure that a small amount on my pits is ok.