Absolutly with you on this, NQC. I know I'd feel odd and tbh, I think you should not feel obligated to do it.
I am of the short sighted, don't wear glasses in pool group, so can see where you are coming from, no pun intended.
I like swimming, and go to the pool quite a lot with ds2. After he has his swimming lesson, I get changed and join him in the water. This means that mums and dads who have been watching the lesson get to see me in a swimsuit which feels a tiny bit odd, but ok as the water comes up to my shoulders once I am in the water.
But you've got to stand around in shallow water, so quite a different matter!
I also belong to an all year round outdoor swimming club - we go to our local lido (not in the winter, though). The pool has a special early morning session for the club so I can get in a nice quiet swim. It is very refreshing.
I am often the only woman - most club members are men between 40 - 70 ( some of them rather nice ). They are all very friendly and chatty and keep inviting me to go into the communal shower afterwards to stand under the showers to wash out the chlorine from my swimsuit. It is a very practical idea, but I know other people (men) would be using the shower with me and it just feels too odd. I make an excuse and rinse out my wetsuit at home.
I think you could consider wearing a wetsuit in the pool. I bought a wetsuit to wear in the cooler months, to keep warm but also to preserve my modesty. (Cool water does rather dramatic things to nipples). The wetsuit stops just above my knees and elbows and I feel much beter in it. As you get towards the summer months you can pick up wetsuit quite cheaply - I heard tescos were doing them for £15.00 last year. I have seen several swimming instructors wearing these types of wetsuits in our pool. You could check with your pool first to see if its acceptable.
I also think you could get away with wearing a T shirt over your swimsuit or shorts. I have seen lots of swimming instructors and some parents doing this both for standing at the side instructing or going into the water. I've also seen lots of swimmers wear a short sarong in the water, which looks lovely.
So if you decide to go with your male friend , I think you have lots of covering-up options. You could easily end up with an outfit that is no more revealing than what you'd wear on a sunny beach.
But honestly, if you still feel odd about it, You Are Not Being Unreasonable to say NO.