Guys, have you ever looked up the ampacity of 18ga wire???
20ga wire will _easily_ carry the current needed to run a fan. The voltage drop won't even be too bad if the length is less than a few 10s of feet.
When following the NEC (as well as good engineering practise), circuit conductors need to be sized to carry the load current, to have long useful life without failure, to survive expected faults, to remain safe even in fault conditions, etc. If you give up all of these various safety enhancements, you will still have a system that works.
If running 16A through 14ga wire resulted in instant fire, there would not be all that many hack electricians around,
and we would never be able to have fun discussions about tap conductor rules.