First off, a fuse like that might be hard to get, you might be able to replace it with a standard 20mm fuse, you could solder wires to each end and solder them to the board, its a tricky job as the fusewire in the fuse can break doing this, putting the whole thing in some tubing to insulate it is a good idea.
And the socket, I would solder it back on without caring if the connections bridge, then come back with some desoldering braid to clean up and remove the shorts.
If you cant manage it the oiutside 2 connections are the power, you could hard wire the power supply direct to the camera, permanently attaching the power supply lead.
Glad to have helped.