So I grab a rook instead. Did I break a rule?
No, the FIDE Laws of Chess are very clear. The choice of piece is not decided until it touches the promotion square.
In so far as touch move applies to promotion the key is that the promotion must be performed with one hand. That is the same hand must be used to remove the pawn from the board (it does not have to be first moved to the promotion square) and to place the promotion piece on the board. How the piece reaches the "moving hand" is irrelevant. It may be transferred from the other hand. If a piece is captured in the act of promotion it must be removed also with the same "moving hand".
4.4 If a player having the move:
4.4.4 promotes a pawn, the choice of the piece is finalised when the piece has touched the square of promotion.
4.6 The act of promotion may be performed in various ways:
4.6.1 the pawn does not have to be placed on the square of arrival,
4.6.2 removing the pawn and putting the new piece on the square of promotion may occur in any order.
4.6.3 If an opponent’s piece stands on the square of promotion, it must be captured.
7.5.4 If a player uses two hands to make a single move (for example in case of castling, capturing or promotion) and pressed the clock, it shall be considered and penalized as if an illegal move.