But the smallest can of naphtha I've found is a US quart and cost $8US off the shelf from a harware store paint department.
That's "VPN", varnisher and painter's naptha- not as refined as the stuff in lighter fluid. If you put some on a sheet of glass and let it evaporate, it will leave a residue, same as it will on your shutter parts. Rosignol lighter fluid is cheap and cleaner, but I use electronic parts cleaner instead. It's an spray can with the usual red plastic tube , similar to the one WD40 has, and can be sprayed into the cable release hole on the shutter. I've also used alcohol, with some success.

None of these is the equal of a real cleaning, however. Go for the CLA, from any number of good shops, and replace the glass on the shutter rather than buying a whole new deal. If nothing else, you may be able to trade the newly cleaned shutter toward a different lens :-)