You might have, or can inexpensively buy, a mechanical pencil which has the feeder button ... Perhaps one of those really large drafting lead holders could be repurposed as a solder dispenser ...

The second version of the Modern Fuel mechanical ... choice of your pencil being made of titanium, copper, bronze, and stainless steel. It can also fit 0.5mm, 0.7mm, and 0.9mm lead sizes for ...