Being able to substitute another ball has been one of the most requested items for years. It's not going to happen. The game was programmed with only one ball, your ball of choice, in the bag at the start of the game. The default to the free ball is is an add-on that was hard-coded into the game so players would not be disqualified when the ball of choice was gone.. To program an in-game choice would most likely cause all kinds of problems with game performance in addition to the problems people are already experiencing.
You do have the option of deleting those balls from your inventory if you are playing the PC version of the game. In the mobile game, just use the odds and ends up in unimportant rounds like practice and CTTH.
It's the player's responsibility to have the bag stocked properly before teeing off on the first hole. Make sure you have a threshold you start with that ensures you won't run out, say, two or three sleeves. Don't ever start a round with less than that and you'll never have a problem.