I’d contact a local swimming instructor because they often film their students underwater with the pool’s permission. One session with them would probably work?
Different pool have different rules, maybe ring some of your other local pools and explain your requirements. Our current pool allows photos and videos, our old one didn’t.
My son is a competitive swimmer and I recorded loads for his GCSE PE at various competitions, different strokes. His coach also had to sign to say they confirm it is him.
You can film it yourself.
Get a copy of the success criteria and get him to complete the skills .
As a PE teacher I’ve seen this happen before with other sports
My daughter used football as one of hers. We didn't get a chance to film her due to postponed matches so her PE teacher gave her a form for her coach to complete. If they won't allow filming can his instructors complete a form ticking off his abilities?
My daughter used footage from her football games. We asked the parents permission.
This year we’ve been asked if we mind someone filming for their daughter x