Yes it's hard when you're shy. Nothing for it but to screw up your courage and just do it.
If it helps, have an excuse ready for why you have to leave, then go along to the first meeting with the idea of talking to the course/group leader to find out what it's about for half hour, then make your excuses and leave. It doesn't feel so daunting to commit to half hour and only speaking to one person. If you're enjoying it you can stay and talk to more people, but you needn't commit to that from the outset.
If you decide to get involved and go back, ask the group leader to introduce you to some people once you get there. Most people, if someone is introduced, will make an effort to chat to them. And most organisers faced with that request would have the sense to introduce you to someone chatty and friendly in the first place. At least you'll have one thing in common, the reason for the group.
You don't have to stay forever either. Maybe mentally commit to 6 months to give the group a chance then if you're not liking the activities or people, or if you're feeling bored, try a different group. Obviously if there's bullying or anything then just get out of there, life's too short for nonsense like that.
Also do a trial run first so the journey and venue are familiar. It takes away some of the first day nerves to know you're not going to get lost, be late or accidentally wander into the wrong place. All of which can make you feel flustered. So best to get it out of the way on a different day.
Don't feel bad if your health means you can't last the whole group out. If eg an hour is your limit then you need to rest/go home, just say so. Nobody is going to mind (and if they do they're a knob, so who cares what they think).
Give it a try, you'll be fine once you get into it. I moved around a lot so I know how it is, being the new person. You get used to it and it gets easier with practice. My best tip is not to focus on yourself and how you're being, focus on the activity and getting to know the other people. Good luck!