Nickerson is big, but note it is several campgrounds in one. The section that is the far-est from the main section has a very different feel from the rest. I say forget about stealth camping on the Cape.
Mass Audubon has a small CG in Wellfleet. In high summer they rent by the week only, in fall you can rent for a weekend. You are supposed to be a member for more than a year to make a reservation.
the "North of Highland" campground generally gets good reviews. Shawme Crowell, just barely on the Cape is an option. Personally, I'd go with nickerson because the central location and being right on the bike path.
JR