How is it possible to remove the string pegs without damaging them?

loosen the strings, put your hand in the sound hole and push the pegs out of the body, or get a string winder and it should have a little cut out to remove pegs, both ways don't damage the peg
You could get a string winder, which also doubles as a bridge pin remover. However, I use just a pair of pliers to kind of wiggle them out. Don't wiggle or tug too much. Just turn the peg slightly, and it should loosen out enough for you to take it out with your fingers. If you tug at it, it will probably come flying out, which could damage it.
Happy Playing!