If you are planning on replacing your shower surround, plan on a messy job. Depending on what type of surround you are removing, it may come off cleanly, but don’t bet on it. I’ve never had a lot of luck removing a surround and keeping the green board intact. The surround is glued or mortared onto the walls and it isn’t supposed to come down easily, so don’t expect it to.
The best you can hope for is minimal damage. When I say minimal, I mean torn paper on the green board face. You will likely have dried glue or mortar sticking to the green board when the surround is removed. It really depends on the type of surround you are removing.
The best chance you have for “minimal damage” is if you are removing a fiberglass surround. You can start peeling it up and keep gently peeling in the hopes it doesn’t start taking a chunk of the drywall with it. You can try using a stiff putty knife to try to sever the bond between the drywall and the surround.
If you have a tile surround, good luck not damaging the drywall. I say this because it is difficult removing ceramic tile that has been mortared or glued to the wall without making holes in it. You may find it easier to pull down the surround and the green board along with it, then reinstall new green board in its place before installing the new surround.