Kids these days feel such pressure to fit in, if it is something you think that bothers her I would go ahead and let her shave, sure its scary but if you teach her how to do it and it helps with her self esteem then it may be worth it. I would be afraid to use a depilitory or a bleach on her, its so harsh on sensitive skin. I have dark hair on very fair skin, I do not recall how young I was, but I know I was shaving by 4th grade.
My daughter is very shy, I find she doesn't do well in big groups of kids, I think she does a lot better if she gets to invite only a few friends over instead of a whole "gang" that seem to overwhelm her. I usually encourage her to go play but also have activities that require some assistance to help move the time along. You can find really cute craft activities for reasonable prices at Michaels and even Walmart has an aisle that sells the foam crowns and visors that can be easily decorated.
Does the school offer any skate parties, or even little festivals where you can go as a family and she can get a chance to mingle? Knowing that mom is a safe distance away can help aleviate some of the nervousness.
It is ok to only have a few friends, I still suffer from some anxiety of meeting new people as an adult, help her with her self confidence and give her time. I would encourage her to keep going to the church youth program, even if they are not kids she goes to school with...maybe offer to let her invite a couple of those girls from her youth group to a fun day outing, movie and lunch? Or if you are brave offer to host a sleep over...just be ready with activities to help the night move along so your daughter will not feel like she is on the spot. They have a lot of cute games that are made in kiddy versions, you wouldn't necesarily have to go out and buy board games either just look up the rules in advance for fun games like a kid friendly pictionary, card games like go fishn or old maid I know it seems old fasioned maybe but its something to keep them occupied and they will have fun, you could even make it an indoor camp out and make smores. I hope you get some good responses, my daughter is the same age and I feel like she would rather stay in the shadows most of the time too, she has her first good friend and I see her really coming out of her shell this school year. I wish your daughter happiness = ) Learning to be comfortable in your own skin can be a lifetime challenge.