You *absolutely* want to use a swim diaper, rather than a regular diaper.
I've only ever seen one brand of disposable swim dipes, something like Little Swimmers? We bought some while traveling, with Tigger on them, just in case we ran into a pool with a problem with reusable swim dipes. I think he wore them once. They were awful, just so flimsy, and if he HAD had a poop accident (he never does "go" while in the pool, he's just never been that way), I have NO clue as to how they would have held it in.
However, Target carries WONDERFUL cloth-based swim diapers, the brand is iPlay. They are usually on the "endcap" area, the end of the aisles, somewhere near-ish the potties and *infant* clothes and booties, pacifier, sort of section (NOT right in the clothing area). They will usually have a "speedo" style, and a "trunk" style for boys, and some will be sets with a sun hat and a shirt. Your kiddo looks good-sized; my guy was pretty skinny b/c he kept growing taller rather than rounder, BUT the infant trunk-style cut off his circulation and turned his legs purple inside a few minutes. I grabbed the speedo-style from my bag, changed him into it, and it was much better. So we got those style each time he needed a new size pair.
They have terry cloth inside, but the inner workings are likely a polyurethane coated cotton, and the elastic is very good. If he'd pooped in those, I can't see how it would have gotten out, which is pretty much the point of swim diapers!
Regardless, don't let him wear regular dipes, not cloth (which we used exclusively) or disposable, in or near water. In water it's dangerous, and near water it's just a big soggy, boggy, big-bottomed mess!
Have fun!!!!!!!!!!!