Your dream of flying is closer than you imagine. By far our highest recommendation, as Rio is one of the few tropical cities in the world where you can hang glide or paraglide over the city and land on a beach. And no, it is not dangerous, (but will kick your adrenaline sky high, no pun).
Regardless of the weather you should call as soon as you arrive and ask to be on stand by, as the favorable wind conditions have little to do with how sunny it is. No training or special gear needed (other than sports-shoes, no sandals), just a shit load of guts.
To fly like a bird you can contact the Sky Center Team (responsible and professional instructors). They offer both hang gliding and paragliding, as well as free transfer to and from your hotel. Safety (they only fly on good wind conditions, so it won’t be a short flight) and satisfaction guaranteed.