When using the enamelled wire (or the thin ex-mouse stuff) you will have a soldered bit where it joins the LED leg. Remember to paint this bare bit with a few layers of enamel paint to give the required insulation from the brass bits. Heatshrink sleeving, should do the job much better from the point of view that it is much tougher than paint, but has the downside that it may not fit. The enamel on the motor wire will traditionally have two conflicting properties - where you need to remove the insulation, it will be as tough as old shoe leather, but where it is vital that it remain intact, it will be as brittle as glass.
The best bet might be to use heatshrink for the bits either side of the join, and paint the join.
The earth sleeving suggested will probably fit nicely over the outside of the brass, but I doubt it will fit up the inside of a 2mm tube.