Stretching the tournament rules, re: capturing pieces Building on this question about tournament etiquette:
What is the etiquette (or tournament rule) for the act of capturing a piece?

Suppose I want to capture a piece but am not sure which of my pieces I'd like to capture with. Is it legal to remove the opponent's piece from the board, then think for 15 minutes before completing the move (i.e., placing my chosen piece on the square previously occupied by the enemy) and pressing the clock?

I know it's probably disconcerting to my opponent (and not good etiquette). I wouldn't do this intentionally. At this point I'm just asking about legality.
Your opponent has the right to view the board also when it is your turn. If you did this and your opponent complained to the arbiter after a minute or two you would face sanctions. Probably just a warning for a first offence, then a time penalty and if you continue repeating the tactic eventually you would forfeit the game. This loss would be graded as such.