I like the solid wire since it is easier to form into a shape and have it stay put. I can route it away from pinch points and it will stay there. I don't worry about the current carrying capability of the stranded wire versus solid wire cause my LEDs are running at such a low frequency (not much of a skin effect). I would advise against using either magnet wire or teflon coated wire in applications where fret abrasion or physical pressure is a concern. But you can always slip shrink tubing or other insulation over the coated magnet wire for extra protection if there is a pressure point.
Stranded wire or flex circuits are better in situations where there is movement. The solid wire will fatigue and eventually fail.
Where do you get shrink that small? We can only find 1/16" shrink.