Same but i feel many sports are weird in that i’ve never been convinced that there’s a particularly natural right or left handedness to them.
Eg. For pool does the more dextrous hand need to push the cue or does it line up and guide the front of the cue? I can see tradeoffs each way and the front hand is certainly not just limp when playing.
Hockey is similar. The top or the bottom hand being the more dextrous probably has tradeoffs but I don’t see either grip as being more or less natural for handedness. I don’t play hockey but play golf and cricket which have similar grips and am similar there to you too.
Golf and baseball batting have obvious handedness - the muscles that pull your towards your centerline and then across your body and significantly stronger than the ones that push your arm back out away from your body, and the right-handed stance in these two sports uses the stronger muscles in the right arm.
My dad was a lefty and played golf right-handed. It's a common enough thing.
In golf, strength is overrated until you get to the pros.
phil mickelson, easily the most famous left handed golfer, is right-handed but plays lefty because he would stand across from his dad and mirror his swing as a kid
fun fact: vs the US, golf stores in Canada carry more left-handed clubs because a right handed hockey player has their right hand higher on the stick which is the same orientation as the grip for left-handed golfers.
Re: pool, definitely the one pushing needs to be the dominant hand.
It has the most degrees of freedom, and more motion. The one in front has a whole table for stability.
But that's just like my opinion, man.