Hi,
Very thin wires are used to connect IC chip dies to package pins. When higher current is required multiple wires will be used, sometimes brought out to separate pins.
So one way to get a higher current rating is to use parallel wires of the same diameter.
Very short runs of 2 inches can be done with much finer wire than say 2 feet. The whole ballgame is how much surface area vs how much power in the wire considering the voltage drop and current, and how much heat is conducted out of the ends and how much heat sinking at the ends.
The fusing current for a #32 gauge (AWG) wire is about 7 amps, and that roughly doubles for every 4 wires sizes lower, so #28 would be about 14 amps. So you'll have to stay under that rating and see if the application can put up with the extra resistance because of the increase in resistance with temperature, and also to make sure that it doesnt get so hot that it starts a fire.
Testing isnt too hard to do however. All you have to do is pump some current through the wire and see how hot it gets
This is easy to do with a decent power supply, or with a big battery and a suitable power resistor.
The best test is done right in the application itself, after it is fully assembled and enclosed. After running for a few hours if the wire gets too hot it's a no go of course. This is better than trying to calculate the right size because it's hard to figure out the real amount of cooling that the wire will (or will not) get.
A fan will help too of course, and for very short runs if the ends are connected to large chunks of metal that will help too because they act like heat sinks.
Solder though is not a very good conductor of current. It's about 5 times worse than copper if i rem right. So any joints should have the wires touching before the solder is applied. This usually means twisting the two wires to be joined or using a PC card with a hole drilled into it where the wire is pushed through and bent over on the copper foil side.