In reply to tcn_2002:
You can't escape duty of care level responsibility for each other (the less experienced person still has a duty of care towards the more experienced too) and it exists for pretty much everything you do inside of climbing or out.
You can however escape additional responsibilities being placed onto people though by not having any individual named as being responsible things like first aid, HSE etc on meets. Having a responsible person becomes a bit of a nightmare if anything goes wrong. This is one of the reasons that a lot of clubs (and the MCofS / BMC) changed to become PLCs rather than less formal groups - it limits their formal liabilities as individuals.
The Duty of Care level "responsibility" has been through the courts a couple of times and never resulted in prosecutions / formal blame (at the time I attended the MCofS clubs seminar anyway) so definitely don't take on additional responsibilities based on the idea you've already got some. Theres actually very little to worry about interms of legal responsibilities provided your informally organised (i.e. not formally in charge, instructing, coaching etc).
Talking to your uni sports association would be a good idea. We got ours to waive a couple of requirements that made sense for other types of clubs (e.g. rugby, football etc) but didn't for climbing / mountaineering type activities. The designated 1st aider sounds like one of these - it would makes sense at football training and matches, but really doesn't work when your divided up into 2 or threes and spread over a couple of hundred square KMs......
Ignoring them and hoping you slide under the radar is fine until something goes wrong and you get asked things like "where was the first aider" and have to reply "15 miles away on a different mountain / in the pub with everyone else etc".
Providing cheap first aid courses for your members so that there's an informal pool of first aiders and enough that there's more than likely a few on each trip is a good way to do it. Much better than making an individual formally responsible for it.
Cheers,
Stuart