Is it ok to go on a swim with your colleagues while on a conference?
It happens all the time, and I see no problem whatsoever. I can understand that you might feel uneasy with your supervisor joining, but nevertheless, I do not think it is inappropriate in any way (we are talking about a normal beach where also families would go, right?).
Besides, a beach is a public place, so even if you somehow wanted to prevent your supervisor from going, you cannot really forbid them to go to the same public place.
Therefore, to address the second part of the question, I think the only option for you would be to refrain from going with the group.
I'm quite insecure how to behave
I'll skip right past the issue about whether it is appropriate to go to the beach with your colleagues or your supervisor. Obviously some people deem it to be appropriate, and we probably will find other people who would suggest it to be inappropriate.
Your issue is that you are feeling uncomfortable about (aspects of) it, for whatever reasons, which are completely irrelevant. It is for nobody else to judge whether your feelings are appropriate or not, they are what they are.
The proper approach then, is clear:
- Don't go swimming to the beach.
- Do not, under any circumstance, feel bad about it. Not everybody has to do everything. Not everybody has to like everything. You do not need to be a herd animal.
- Do not fall into the trap of explaining to anybody why you don't go. Just don't go. Don't talk it through with your colleagues.
This advice has one specific reasoning: by deciding on one particular action, and sticking with it, you remove your own insecurity. You now can act with confidence.
It does not matter whatsoever that there may be naked skin involved here. I would give the exact same advice if it were about doing a mountain hike (with you being afraid of heights) or a trip to the bowling alley (with you just having no fun whatsoever at bowling), or a Dungeons&Dragons roleplaying session, or whatever else.
It is also a good exercise; it helps to get into the habit of deciding your own likes and dislikes and sticking to them.
Oh, and if you need some objective reasoning of why it may be appropriate to stay away: there always is the concept of separating work and private life. You never need to be ashamed if you want to keep this separation up. Different people have different scales of where that separation has to be. You pick yours, and stick to them. You can still laugh with your colleagues and wish them fun at the beach.
In my mind the answer to your first question is pretty simple. Yes, of course it is okay to go on a swim with your colleagues. Our colleagues are often our friends and we are allowed to socialize with them. While some universities have rules about dating/sex between faculty/students, there isn't any western university that would prohibit going to the beach.
The answer to your second question is what to do if someone you do not want to show up, shows up. If you think about it in general terms, this can happen at the beach, the bar, or even lunch. A swim at the beach is is in some ways easier to deal with, compared to a bar or lunch, in that it is clearly a social activity and one in which it is likely someone might behave in a non-professional manner (in this case clothing choices).
I suggest you talk to the colleagues you want to go to the beach with and suggest it be post doc only, or whatever rules apply (e.g., student only, non faculty, or assistant professor only) that keeps out the people you want. This has the advantage of not singling anyone out and realistically, there may be a whole "class" of people you would not want to swim with. As long as your rules are not overly discriminatory (e.g., let's keep the blacks out), I doubt you will have much resistance. In fact, my guess is you are not the only one to be concerned. If you do get resistance, then you should assume that it will be a group that you will be uncomfortable with. If you do set rules and someone breaks them, you should call them out even if you are not uncomfortable since someone else in the group might be.