I have actually tried that with the soldering iron years ago. It is terribly difficult to get it to stay on it and it doesn't have enough thermal mass to heat the joint very well. MacGuyer could build a mainframe with it to defeat a bad guy but I couldn't
WRT solder, RS sell multicore 0.8mm leaded but it's not cheap!
Chemtronics Soder-Wick is worth spending on over doing your own braid - the stuff is about £3.50 a roll from RS but is far superior to all other brands and methods I've tried.