I think it's probably fine. I've been using GermX for a couple years now and haven't noticed any effects. At best the smell might be a mile irritant, but I'm not even sure of that. It's probably no worse than the gazillion fragrant anti-bacterial handsoaps that exist.
The main ingredient in GermX and most other hand sanitizers that smells so strongly is ethyl alcohol. Ethyl alcohol evaporates quite quickly, which is why your hands dry so quickly when you use hand sanitizer as opposed to just rubbing water on them. Even though the smell is pretty strong right at first, at least for me, it seems to wear off pretty quickly until it's faint.
With hand sanitizers being so common there is bound to be information about pet safety if you search on Google. Since it is designed to come into contact with humans, I doubt there's anything toxic about it. You could also always get an ingredient list and look up the MSDS protocols for the chemicals.