I too was a very poor swimmer, and I had to do pool drills (vest and dinghy) for my work (helo flight test).
The dunker scared the poo out of me, especially the turn you upside down, in the dark, without time to properly strap in part. We also had to do sea survival and wet winching, jumping into any water was something I had never been able to do, jumping into the sea also scared the poo out of me (I actually froze up and couldn't do it, had to go back for a second go).
I did a course of adult swimming lessons, the only people in the pool were the adult non-swimmers (shallow end) and the adult improvers (including me), in the deep end (only about 1.5 m at my pool).
Go for the adult lessons, they are very good, I felt a bit embarrassed at first, but so did everyone else. Since taking those lessons (12 weeks or so of them) I have so much more water confidence, and now scuba dive as a hobby (including plenty of jumping off the back of boats), swim for exercise and the last two times I did the dunker I really enjoyed it.