If the button is sewn on - I'd recommend you to resew it manually and firmly (don't spare the thread). Also you can resew it closer to the edge to give a little bit of extra room.
And you can carry a threaded needle in these shorts (probably put in some container... like a syringe needle cap or smthn) and spare button in case sewn button will break (but at this point I think wearing those would be painfully uncomfortable). So you can excuse yourself to the men's room and just resew it there.
If the button is like in jeans - when those pop they might rip off the fabric and ruin your shorts. But popping those require quite a force, so once again you shouldn't have been wearing shorts that tight by then.
And another option is to just leave it unbuttoned and cover with a belt. I did that and its not that bad. If you have a big overhang - thats an extra bonus there for stealth