I was wrong. Wrong about the necessity of hands for gesturing (actually, for waving, to be exact).
Apparently, any old hook will do instead of hands. Or should we say that this case is a special case of projection? Perhaps it is the placement of the hook on Pirate Arm’s End that enables the illusions? We have no problem seeing gestures because the hook is clearly a substitute hand?
Would the magic disappear if the hook was alone, without an arm attached? Perhaps it will and perhaps it won’t. One thing is for sure though, my hopeless over-analyzing of anything gestural is killing this otherwise decent joke.