Just apply the tip of a soldering iron to the solder joint at the 510 and it should come off ,then you should be able to push the 510 out.
Personally I wouldn't use wet/dry paper for what you want to do,I'd try and find/use very fine sandpaper instead.
I don't see him soldering the 510 after press fitting it, my guess would be it's press fitted from the inside after all soldering was done.