All of the Celliwig people in the party would try to stop him (and possibly some player characters, but I can't speak for them) so he may find that to be an incredibly difficult task. If you still want to go forward with it, there's a good chance he's going to get arrested and/or stabbed and sent back to Camelot. Especially with everyone jammed into the same cave, he would definitely be putting others in danger too.

If you think he can overcome all the Celliwig people and the dragon and any player characters who may interfere, then let us know we will discuss his punishment because despite Beowulf's enthusiasm for slaying dragons, they sacred creatures here in Avalon. There will definitely be consequences!