Long ago when my wife and I moved into our house, after we moved Kaybee the cat in, I witnessed a mouse run from under the dishwasher over to the cat's dish, steal a piece of food, and run back.
I went and got the cat, took him to the kitchen, and sat on the floor with him to show him the mouse. The mouse repeated the theft, but Kaybee was still too freaked out from the change of residence to react.
A few days later I found a dead mouse on the floor with a piece of cat food in its mouth. I interpreted that as Kaybee's way of saying, "I'm back on duty. All you mouse bastards are on notice."
When my cats are going after bugs, I usually try to catch the bug first and take it outside. Unless I catch them messing with a wasp, in which case I try to trap and swat it with something heavy so that they don't get themselves stung
I trade finding bugs for treats. Cat tracks and alerts, I catch or kill, and cat gets a snack. Everyone wins and no one gets bitten, stung, or weird parasites.
I used to have a dog that would attack scorpions. It looked like he was getting stung in the face a dozen times over, but he never whimpered nor had any swelling, so I think he was just fast enough to avoid the stinger. This has nothing to do with your story, I just randomly thought about it when I read about your adventures with wasps.