Assuming you solder in the vicinity of your computer...
This is not professional grade by any means, but if you just need to keep the fumes from going right up your nostrils you can use a simple 5v DC fan (cost $3 - $4 typically) and connect it to an old cut USB cable you have hanging around and let your PC to run it.
Basically the outside pins of the USB port it is plugged into run it. Pin 1 should be 5v and pin 4 should be ground. The fan will probably be something like 0.20A, which should easily be pushed by a USB 1.0 or 2.0 port which I think deliver 0.50A. Throw a SPST switch in the power wire and you don't have to plug and unplug it all the time.
It's quick and dirty, but it's cheap and keeps the fumes out of your nostrils. It can easily be double side taped, clipped to helping hands, etc., anywhere you need it.
NOTE: I bought a 5v fan and have an old USB cable, but I haven't actually made this yet. It's currently just based on a a thought I had while looking at PC fans recently. I'll give it a try in the next day or two to see how / if it works and let you know.