Here's how to screen mirror your iPad to an AppleTV but using a Bluetooth speaker instead of TV speakers/projector:

1. First pair your Bluetooth speaker to your AppleTV. Put your Bluetooth speaker in pairing mode > open Settings on Apple TV using the silver AppleTV remote > tap on Remote and Devices > Bluetooth > Pair your Bluetooth speaker

2. Now screen mirror your iPad to your AppleTV like you normally do and when sound is played it will come from the Bluetooth speaker and not from your TV/projector speakers.