Thinking some more about this @Thoughtfulgolondrina.
There are two things I have been determined that my very young (4yo) DS should get to grips with this year. One is swimming and the other is speaking English (we don't live in the UK).
I decided to push these things because I don't want him to be able to remember ever not knowing how to swim or speak English. But from my point of view, it has been a lot of hard work over a sustained period of time, and I will remember how much effort it took even if he doesn't.
The biggest problem with teaching a very young child a new skill, in my opinion, is motivation. If something is difficult and they don't understand why they need to be able to do it, they will resist. They will resist until they can do it, and then once they can do it they will think it is super cool that they can do it.
Your DS has the motivation to learn to swim because he wants to go on this school trip. He understands that it is something he should learn to do.
I've read a lot of threads on Mumsnet about the optimal age for teaching children to swim and many people have said it's a waste of time and money teaching very little children to swim because it takes years, whereas the ones who start a bit later catch on much more quickly. On the other hand, I think adults who cannot swim tend to assume that it is too late for them.
Don't let your DS become an adult who cannot swim. The best time for him to learn was a few years ago. The second best time is today.
Stop making it a bigger deal than it needs to be.
Take him to the pool this afternoon. Explain that filling your lungs with air will help you float and that kicking your legs will help you propel through the water. Watch YouTube videos about learning how to swim.
He wants to do it, so tell him that you're going to teach him, it's not rocket science, and there's no reason why he shouldn't be able to swim in the next three weeks if you take him to the pool as often as possible and work at it.