Yes, 15A would be fine. Many tools only pull that under intense load, and the power cord couldn't care less. Might get a little warm.
I use to pull 30A through a 12ga extension cord for hours at a time, the problem is not the cord, it's the connectors on the ends which are crimped. If they aren't crimped well, that's what gets hot, not the conductors. You could pull 15A through 18 gauge wire over 75 feet, keep the insulation nice and warm and supple.
(actually, you'd only lose about 100 watts, or about 1 W/foot.
thanks guys for confirming