Well, if not board shorts and not Lycra/spandex => polyester jammers!!! They will last forever! I mean, if you're going to wear cycling shorts in public, that's practically the same thing (without the pad).
Probably not the response you were looking for, but if you don't want to wear elastic trunks, and you don't want to wear loose trunks, then that kind of only leaves nudity?
you could try swimming in the running shorts that have a compression-type liner and then somewhat looser shorts over. I don't think this would be an improvement on board shorts, though.
Yanti Ardie of Y Tri Multisport & Majick Juice for lasting critter defense & skin soothing
~ World Open Water Swimming Association Coach & Official
~ IRONMAN Certified Coach (Founding Member)
~ Triathlon Australia Professional Development Coach
~ 3 by the Sea: my Journey from death to ...