remove if theres screw and solder the cable in. Shud not have any problem on the connectivity. The most important is the wire solder to the tip and sleeve point correctly within the plug. If cannot removed screws, heh, just solder the cable over it, but have to make sure the cover can close back properly that is...
some cheapo plug dont even bother to have the point for the ground connection, those can just solder anywhere within the enclosure and make sure its connected to the sleeve.
another thing when wiring cable, it be useful to have a small multimeter around. Everytime when you solder finish or wanna test whether is it working, just do the continuity testing and listen to the beep. It can save lotsa time when you wanna find out where is the cause of failure along the cable/plug if it doesnt work.
This one not a must though, just thought i mentioned cause when i started with those cable soldering, i reallised everytime when the cable fail me, i be turning round in circle not knowing where to check and star to get frustrated. Then the multimeter came in and it make life easier to trace everytime when the cable failed, either bad/cold joint in the plug or somewhere inside the cable, theres a break of some sort..