Drill out the flash hole first (keywords: "flash hole uniformer"), then decap as normal.
The primer is probably crimped in place, which is a separate issue, and (yes) will make "normal" decapping harder. When that gets tough, I use a Lee hand decapper, or the decapping parts from a Lee hand reloader in one of the .22 centerfire calibers. If you don't have the hand reloader, and don't want to buy one (or can't find it in stock), you can order the separate .22 hand decapping stem&pin from Lee, as a part. Or use a universal decapper, per the post above.
Then, of course, you have to remove the primer crimp.
Yes, it's a major PITA. Ask me how I know.
P.S. -- you wrote:
Well, there goes THAT idea ...
FWIW, brass usually sells better if the primer is left in, because the primer carries some information about firing history. In particular, if the primer is still obviously crimped in, you can figure the brass is once-fired, which is more valuable. (Except Igman, I guess.)