I believe the reason you won't find that mentioned is because it isn't mentioned.
Therefore, the correct mechanic in this case is to do what other officials in your area do.
The purpose of the whistle in these cases is to alert players that play is about to start again after a delay, whether it's a TO, injury, or other type of unusual delay. There are many that feel it becomes much more obvious in a FT situation that play is about to start when you announce the number of FT's and then bounce the ball to the shooter, so a whistle in that situation seems a little much. I know it is not done in my area, and it is not done at the NCAA level.