Yes, it is perfectly safe to lick girls armpits, and you are in good company, it seems Robert Pattinson is a fan too, apparently he used to lick Kirsten Stewart's armpits.
I guess some girls would find it strange, and you may get a few refusals... Therefore, try to introduce this urge gradually, though I am sure that a girl who has feelings for you would understand.
I have to admit that it's quite a new one to me and I have never tried it. However, there are far stranger things out there and it is harmless.
Am I right in thinking that armpit licking is better when there is no deodorant? If so, that has to be safer because deodorant is toxic (though in such a small amount it may well be okay).
Deodorant will dry your tongue too, so I doubt that sensation would feel sexy.
So yes, lick away, enjoy, You aren't going to harm yourself and you're not hurting anyone else either.