I have a condition in my hand and feet that cost me my toes and regularly prevent me from using my hands. Because my balance is compromised, I now sit down in the shower stall (it makes cleaning the shower stall after showering a lot easier too, incidentally - hint hint). But that also means when my hands are bad, I can't use them to sit down on the floor or get back up.
I developed this technique to sit down and back up without hands: to sit down, I thrust my arms forward and sort of start crossing my legs and bending my knees at the same time, ending up sitting cross-legged in one smooth motion.
To get back up, again I thrust my arms forward, put my right foot under my butt, use my left leg to ram my right foot backward under my butt as far as it'll go, then start getting up on my right leg alone for a few inches until I can shove my left foot there also and rise up on my knees alone, with my arms forward to keep my balance.
If you have good knees, it's a good technique.