[Hockey Stick] No
[Essential] After quite a lot of thought, No. It's quite important, but not as essential as, say, the ball in football.
[uniquely used] I'm not 100% sure what you mean, but the AOTC is not used in any non-team variant of the sport(s).
[rethinking] No. The circumstances under which two hands are used are a giveaway.
And now you're all just toying with me, I think.
Flouting COVID restrictions, the audience claps one-handed with their neighbours.
It's all yours, CdM, although I'm afraid I haven't got a symbolic object to hand over. Some bugger ran off with it.