Take out the matching screw from the opposite side (or from another cabinet.) Go to Corner Hardware in Brooklyn, on Nostrand Avenue near Avenue I. They have the “Hilman Fastener System” where there are hundreds of different screws and other hardware in little drawers. You can put just one screw into the supplied bags, and write the part # on the bag and take it to the register. I have found dozens of rare screws this way over the past 11 years, since I moved near them.
They used to have even more, but unfortunately, they recently reduced their inventory to save space. Other stores that used to have the same system eliminated it due to shoplifting losses.