I was prescribed testosterone a couple years ago. I remember rubbing it on my inner thighs, and don't remember where else. Except for (brace yourself) my genitals. I did that a couple of times, as my doctor recommended to do that if I wanted to feel extra "frisky." However, if I recall correctly, you're not supposed to rub it on body hair, so if you choose your genitals, make sure you are bare as a baby's tush!
As long as you wash your hands after application, you are fine. I never worried about transferring it to my young kids. Just wash well!