Perhaps a small touch of dielectric contact compound (very cheap) like what they give you when you put a new headlight in your car to make the contact not fail? You get a little tube even when you
buy small auto bulbs to ensure connection.
But this is sticky and might connect the two points always if to much was used.
Better to stay with your idea. A flexable ladies nail file would fix this with two or three hits. Just bend it to a curve shape then you will have a tool handy.
I like the thinking, like you, I am always thinking. Hahaha.