Looking at a number of box fans, the biggest draws 110 Watts on high speed (most draw much less).
That will mean your inverter will draw about 10 Amps to run it - worst case. It's probably closer to 5 or 6 amps.
The wiring in your RV will be fine with that small amount of load assuming nothing else on the circuit draws much.
Normally the circuits in RV are protected by a 15A fuse and the wire is completley capable of supporting that.
So your fan should not be a problem if your running it on the stock wiring.
Relax and enjoy.