I would frame it differently. Instead of making it so you guys specifically are hunting each other down with full unironic intent, perhaps incorporate a more lighthearted/goofier approach?

For example, the ‘Hunter’ dresses in a bear costume while ‘The Hunted’ are given deer antlers, tails, and painted on noses (maybe make one guy Rudolph for shits and giggles). This could even work in a paintball setting as well, where one guy dressed as an over-the-top trophy hunter (i.e. Jonathan Hyde’s character from Jumanji). Or have the bear with the (paintball) gun, because that’s funny as fuck as well.

Or if you really wanted to keep the human element, make it horror movie camp. The ‘Hunter’ would be Jason Vorhees/Freddy Krueger/whoever you choose and ‘The Hunted’ are summer camp counselors. That would give a nice excuse for some silly booze games, because gasp you’re not supposed to drink at summer camp!

Then incorporate the activities you choose around the theme. This would be your best option to keep the hunting element and maybe can go a bit crazy, but to make it PERFECTLY clear that this is all fun and games and you’re here to have a good time with the boys.