Actually, most of the hardware stores DO carry butyl tape just not where you might think it is. Look for a 3-6' long roll, 1-2" wide, in the PLUMBING section or the ELECTRICAL section. I've bought 3M's prime quality "butyl self vulcanizing tape" in Home Depot, right next to the other 3M electrical tapes, it is used to waterproof cable and antenna splices. These tend to harden up over time, not rock hard but layers fuse. Regular butyl "caulking" tape will stay gummier longer.
Sometimes they stock clear silicone tape--which is pretty much the same product, doesn't quite self-fuse as permanently but can be used as a gasket material just as well. Sold in the plumbing sections (along with butyl) as a hose/pipe leak patch material, too.
I'm assuming the tape is going to be laid down flat as a gasket under the hinge panel--not stuffed in the screwhole. Either of these should work as a gasket material, without needing to buy a huge roll from a special place.
I have both self vulcanizing tape and glazing quality butyl ribbon or flat tape sitting in my shop. They are NOT the same product!!!!!!!! I would never even consider using the self vulcanizing tape over the glazing grade butyl.
The stuff I use is very, very, very gooey and sticky and comes stuck between waxed paper as it can not go onto a tape roll or it will be destroyed trying to un-roll it. There are a few grades of things called butyl but self vulcanizing tape IMHO is not one I'd choose for re-bedding deck hardware.
Perhaps in some parts of the country you can find butyl glazing tape in home centers and hardware sotres but not here. RV stores are the only places I've seen the flat version in colors like gray and off white. Again, I would NOT suggest using black if it can be avoided. I used black on my port lights but only because I could not find a source in the diameter needed in gray or white..
Black Round Butyl Tape:
Keeping the black off the gelcoat:
As you can see I used 3M 101 polysulfide to seal the trim ring to the exterior and the butyl to seal the port to the cabin. This kept the black butyl off the gelcoat..