Help with soldering: MICRO wires!

I have a little accessory amp/speaker unit.  3.5 mm plug connection failed the other day.  Need to solder a radio shack replacement plug on the end.  Boy, those wires are MICRO!  Seem like no insulation, only lacquering on the wires and a wisp of a fiber core.  I have tried skinning and shaving the wires with an x-acto blade to no avail.  Can anyone tell me the proper technique to use here?

Sounds like those tiny headphone/earbud wires, usually red,green and gold. Yes, they are like threads!

Don’t worry about the coating on the wires, it should melt off.

Here’s the trick that works for me, it is a reflow solder technique:

Melt a small pool or bead of solder on the plug contact tabs. If they have holes for wires fill them with solder. Working one at a time, remelt the solder pool on one of the tabs and stick the coresponding wire in it while molten. Let it solidify and do the same one at a time procedure on the other two. Let it cool and check operation. The heat of the molten solder should melt the coating on the wires, so you don’t have to remove it. If you have a dead channel or channels, determine with a meter which one is faulty and simply remelt the solder on that connection with the wire in place to hopefully melt the wire coating.

I’ve dealt with several of these types of cables and have only had to try a second time reheat on a couple of them to get connection. Work slow with steady hands, those wires are barely visible!!!

Thanks a lot for the suggestion.  I’ll give it a try.