What would be the best way to carve away the access. Think about a dremel type tool. I am not a woodworker, so I don't have a shop of fancy tools. So I will have to barrow or buy.
Dremel tools, or any power tool for that matter, got no business around gunstocks!

Draw a rough outline of what you want on the blank, cut it out and work it down to the finished dimensions with rasps, plains, spoke shaves, gouges, scrapers and so on.
Me thinks you need to do some study/reading on woodworking and stockmaking This question is kinda like going to a medical forum and saying, "I want to perform some open heart surgery. What's the best way to open the patient's chest? I'm not a doctor, and I don't have a scalpel, but I was thinking of using a circular saw."
Of course, some non-professional gunstock makers can make nice stocks! Even on their first try! Go for it! After all, it's not open heart surgery ya know! But do some independent study first. There's plenty of detailed information out there; a lot of it for free.