Before I was smart enough to know better, I used an XActo knife to fix skips in my father's old jazz records. I used an XActo knife to fix everything back then... But it worked, and I have fixed a dozen over the years. You need very good vision like Wayner says. Just find the skip using the record player, and retrace a new groove through the obstacle. It will never be a perfect silent fix, there will be a noise, but at least you can sing along again.
I've never tried a pin but it should work to plow the existing misplaced vinyl back into position, but I don't know if the vinyl will stay in the corrected position. If not, the sharp blade will cut a new furrow through the vinyl. Use a new "#11" blade with a sharp point. Don't try to do it in one cut, just gentle go over the track you are trying to make a bunch of times until it starts to form.
Other times, the knife tip can remove a piece of dirt that cleaners won't. But I think steam or a better cleaning fluid would probably be safer in that case.
