Can I use a 15-amp extension cord on a 20-amp breaker?

No. Even if your current load is under 15 amps, the breaker allows up to 20 amps before tripping. A surge or added load could push the cord past 15 amps, causing it to overheat and start a fire before the breaker trips. The breaker protects the wall wiring, not the cord. Get a 20-amp rated cord or use a different outlet.