Hi,

If I delete a sound from a map, will anything bad happen when the map runs an action like "Play WAV ''", or will it just be an empty action?

Normally, no, nothing will happen if the map cannot find the wav file / there is no string in the play wav action. There are corner cases where you can get the action to attempt to play a corrupt string, which will crash SC, but it's very rare and finicky to do this, and it's an easy thing to fix if you do it by accident.