so how does your concept of chess-boxing differ from the classical rules?
The boxing and the chess are simultaneous
While it is your turn, your opponent is allowed to punch you. This encourages you to complete your turn quickly.
Upsetting the chess board is a no-no.
perhaps make them call out the move so that they don’t upset the chess board
“Uppercut, left cheek.”
“Fist to Bishop 6”