I am less familiar with the girl scouts than with the boy scouts, but I am assuming the camp focuses a lot on outdoor activities, with gross motor skills, as well as crafting and social skills.
Certainly yoga is a big go to for mind body exploration. Having props is great, but are in no way necessary for a good class. You might look at the Yoga Alliance web site. They are the professional association of yoga instructors and will have a data base of teachers you can check by geographic location as well as by specialization. Look for someone with some background working with youth. I’ve taught that group a bit over the years, though I am in no way an expert with them, and find their needs are a bit different from the average adult group. You can then see if you can find someone who matches what you are able to pay. You could also look for videos, and if you have the equipment do it as a video together. I think that is better than deciding to do yoga without having someone who is trained to teach it.
I also really like karate, if it is focused on self defense. There is a karate place here in RI called Self Defense Training Center where my boys went. I was always impressed on how they taught the kids to have good self image, and how to respond with both strength and restraint to bullying, by teaching them to make eye contact, raise their hands palm out and say loudly ‘leave me alone’. For girls that is just really great for sense of self, which is a part of the mind body continuum.
There is a technique I sometimes use in my mindfulness workshops you might also like. It is called a sensory walk, and involves exercise, sensory awareness, and cognitive function through journaling. You take a walk in nature, but before the walk you explain everyone is to be completely silent, and after the walk everyone will write a few paragraphs on the walk using descriptions of what they encountered with other senses than sight. Typically on the walk I will model reaching out to touch tree bark, or bringing flowers close to my nose to sniff, or turning my head to listen to a bird.
I would also strongly recommend meditation. You aren’t going to get 10 year olds to sit for 30 minutes, but beginning to teach them to still their heart and quiet their mind is really good. Time the practice after something physically demanding and a short yoga or stretch and they will find it easier to do.