Biggest issue new solderers have is putting solder on the tip. You want to heat up the joint and apply solder to that. When you put it on the tip, the solder melts but the joint isn't usually hot enough and you get a cold solder joint.
Best advice I can give for replacing those fuse holders, is to unplug all the jones plugs from the bottom board, take out the bolts holding it to the cabinet, and remove it . Place it on a bench, or sideways across the cabinet (with the playfield removed).
This will allow you much better access to the spot where you need to solder and keep you from having to stand on your head while trying to solder inside a box. The few minutes that it takes to remove it and put it back are well worth it.