As far as whether it's ok/safe to use, I'm sure it's safe to use (well, as long as the product itself is not gimmicky or has electrical failures or something). If it's just blowing air onto your nails, I don't see the harm in that.
I usually just do my nails as I'm watching tv, so they get about 30 minutes to dry before I actually do anything with my hands. A good top coat will help immensely though, because if your polish were to get "touched" by anything, it's just going to disturb the clear later, instead of your actual colored laquer.
I've heard that soaking your nails in ice water for 3 minutes helps them to dry, too, but I haven't tried that one.
I've tried Zoya's drying oil, but I always use Seche Vite on top of my nails, so I'm not sure if I really noticed much of a difference. Multiple thin layers of laquer do dry faster than one thick layer though. I have the hardest problem with cream colors with this. They seem to apply unevenly so even with multiple layers I'll have some parts that are still transparent, but if I apply a thicker layer to try to hide it, it'll still get scratched 24 hours later. If I stick with thin layers that dry faster, it usually works better (some cream colors nails I'll end up doing 5-6 layers because of this instead of my usual 2-3 layers).