Push off with legs from the wall.
Then a long straight glide to next vertical wall, reorientation, and another push.
As though I were in a swimming pool, in the depicted scenario I push off with my legs against the wall and drift through the air. But my aim was off and I wind up to the left of the exit. I reorient myself in the air so as to land legs first. My reorienting does not go so well either and I turn more than planned. When I push off I wind up hitting the cylinder so far to the side I do not have a good angle to get the exit.
I push off again hoping for the cube which has a good flat side. I miss by a mile, but the cylinder is good enough. I push off again aiming for the cube and this time I get it.
My push from the cube is on target and I get to the exit.
Probably I would bounce off stuff in the room many more times than that. But each time, the energy I impart is only what my spindly legs are capable of delivering, and it is no great thing to stop myself with arms or legs when there is something solid in the way. I reorient and push off again.
I might take off my shoes and do this barefoot - I think my sticky bare feet might have better purchase than the shoes. When I hit a vertical surface I have some fake weight for a second or two by virtue of my momentum and I can use this time to reorient with feet on the wall.
I put the shoes in my shirt and tuck it in; don't want to drop them!