Those wires are incredibly bare.
I suggest desoldering it, and making the new exposed wires only large enough to cover the solder point for each.
The reason I say that, take the wire you have your ground and your signal soldered to (the one with the black and red wire), if you jostled them enough, they could touch, and trigger without a button press.
Desolder, measure the exposed wires, cut, resolder make sure its down there good, and hot glue the connection to help.
You only need to strip 2mm off the tip. You then melt a little solder to the tip, the insulation will shrink away from the tip due to heat exposing a mm or so more of wire. You then heat up the pad and then put solder on the pad contact on exposed metal. Only expose the wire that needs to be soldered and nothing more.
Teflon wire was the first type I bought when I wasn’t sure, only 20f though . I hated that stuff instantaneously, the insulation makes it ridiculously un-pliable. However, I never thought of the benefit of not having to deal with backshrink though, that’s pretty awesome. I tin my wires so it backshrinks to a spot where the heat won’t allow it anymore, then I just clip the wire and it works just fine.
On principle, yes, but for this you can just heat the joint back up with an iron and then pull the wire free. Cut a new end on the wire and use whatever solder’s left on the pad to do what rtdzign suggested.
What Icy Black Deep Said, for something like this you really don’t need a solder sucker or braid for this (I honestly hate solder suckers, if you want to invest grab a vacuum desoler tool at Radioshack). That being said, it’d be a nice idea to have the tools, for future use.
Don’t give up! A new USB cord is only four wires, you can do it!
Welcome to the world of soldering! You will have a lot of fun learning.
The other members have made very important statements. I highly recommend using ?helping hands? when tinning wires and soldering pads. A ?helping hands? device can be used to hold wiring, circuit boards, etc via alligator clips; this allows your hands to be free to hold a soldering iron and solder.
Quick Tip: Wrap each clip with electrical tape if you have it on hand; this will lessen the amount of stress or crimp on wire insulation.