Well anyway, here's what you can do. Go on Co-optimus's database
and filter by players (at least 4) and add a filter for co-op campaign. Then have fun there.
I wish you luck for non-Steam games. Chances are if they're from a big publisher, they're going to use DRM like SecureROM anyway. If it's an older game, then you have to cross your fingers that it works on Windows NT 6, especially in the early 2000s if you go that early. They are hokey with anything that isn't Windows XP or below.
As for your friend, if I were you, I'd tell him he can sit out until he installs it. Or you all can go get consoles because those are his only two options, and one of them only affects him.
Well, if he's really super paranoid anal, you can also tell him to setup Sandboxie and run Steam in a sandbox (of course, have fun configuring everything).