I've tried swimming naked like 3 different times, both with items in my hands then truely naked, and it wont trigger the quest objective to be finished. Im swimming in a lake if that matters at all
Try starting with full stamina, having nothing at all in your equipment screen and swimming in deep water, parallel to the shallow water. You have to stay in there several seconds so you want to be right beside the shallow water to get your feet back on the bottom before you drown.