I won’t ask about the ‘why’s’ of this question…...
But, you can of course type with just one hand – several of my colleagues type with only 2 fingers! What sort of utility are you looking for exactly? Would it make the keyboard behave as short-hand (a bit like court-room thingys)?
Sounds like you either need a Stenotype Machine or to perfect your one-handed skills with a normal keyboard. I think Stenotype machines still need two hands, though..
Realistically, won’t hitting the ‘modifier key’ be just as time-consuming as moving your left hand to the right side of the keyboard?
(And to avoid permanently scarring my image of you, I will assume your right arm is in a cast)