Do all the lights need to be controlled individually or do some of them share a supply?
I assume that you are using a common return for all of them with the resistors in the supply side.
The supply current and voltage won't matter, each LED will take as much as it needs which will be just a few milliamps.
Sources of very thin wire are multistrand alarm, computer or telephone wire although not quite so thin as Grain of Wheat wire.
For really thin wire you could use the enamelled type normally used for winding coils which is available in a variery of gauges – have a look at the Maplins website.
Colin
Edited By Colin Bishop, Website Editor on 08/06/2012 09:18:26