I'm not sure what you mean regarding a mill, but this is something that you can do yourself with a variety of wood tools. Since you are planning to camo dip the stock when you are done, you don't have to match the original finsihs, which is a huge plus.
Begin with a file, occilating table sander, or palm sander. Other options are an angle grinder, table mount belt sander or disc sander.
Start off easy taking about 1/32"-1/16" off at a time. Be careful with the power tools. It is easy to get carried away with them.
When you think you are close, switch to coarse sand paper (60-80 grit) to make it smooth. If it feels right, then start working up with your sandpaper grit. Since you are dipping it, you can probably stop at 220 grit. If you get carried away and make a mistake, you can add some epoxy filler and fill it in and sand away again.
I have done similar work like yours to 4 shotgun stocks so far, one from scratch which required a band saw. You can do it unless you are all thumbs when it comes to tools.
Plus, by doing it yourself, you can constantly feel the stock until you like what you have. If you take it somewhere, it may take multiple trips to get what you like, or they will take off the 1/8" you requested and then your done.