My daughter is not a trick rider and she can pick things up off the ground from her pony at a gallop. She is a mounted games rider.
http://www.mountedgames.org/
But beyond that, back to the original question, stirrups are there to help with mounting and staying in the middle of the horse. It is entirely possible to ride without stirrups. Also possible to ride without reins. My pony is largely controlled by my seat and legs, somewhat by my voice, and very little by the reins.
November is no stirrup month. I know a number of folks who are riding without stirrups for the whole month. Most of these are people who never leave the ring, but I would guess the majority of them are jumper types with a smattering of dressage riders thrown in.
Bolero - you have the leg aids backwards. You want your horse to bend around your inside leg, so the outside leg is behind the inside leg to turn.
We ride English and we do use safety stirrups, a very old design with the outside branch of the stirrup bent forward to allow the foot to come out to the side. There are also Peacock stirrups, which have a rubber band in place of the outside branch. Western tapaderos serve a similar safety function by not letting your foot go all the way through the stirrup.