Raymond wroteTo me your play is no different in theory and application than a player tossing the ball up in the air (not a try/not a fumble) and taking steps with both feet and catching the ball in a new spot.
Nice example.
This involves a fumble (muff):
4.44 SITUATION A: A1 attempts to catch the ball while running rapidly. A1 muffs the ball, but succeeds in securing it before it strikes the floor. A1 then begins a dribble, taking several steps between the time the ball was first touched until it was caught. RULING: There has been no violation provided A1, after catching the ball, released the ball to start the dribble before the pivot foot was lifted from the floor. (4-15)
This doesn't involve a fumble:
4.44.3 SITUATION C: A1 throws the ball over the head of B1 and then takes several steps before catching it. RULING: Traveling violation since the ball did not touch the floor, the tossing and subsequent catch is illegal. (9-4)