yes you can cut/solder in a new piece & shrink fit insulation is good (dont forget to slide the piece of it on one of the wires before you pickup the soldering gun). the alt field terminals can go on either way. the plastic types are just a safety bonus to keep something from accidentally touching it & dead shorting it, not required & are OK IF you can seperate the metal terminal inside it so you can solder it or even just cut the plastic from the mini tube part of it where the wire slides in so you can solder the wire there for a good tight secure connection