The OP says:
connected using long wires, which will probably cause inductive load since the LED is toggled at a high rate.
My question is: will the parasitic induction be any different if the LED resistor is located on the PCB or close to the LED?
So, despite being a lone voice, I still say Option 2 would be best to reduce parasitic induction (and capacitance) effects on the switching transistor - and radiated from the wiring.
Of course barely matters in this particular case. But would it make any difference if the circuit was higher power, say a 12v 5A 12 meter PWM controlled LED strip around a ceiling, and the TR a fast switching MOSFET.
Would it still be best to put the resistance in the 12V line in case the 12V gets shorted, and then try to transmit the raw PWM around the room, - I know which option I'd choose if it was in my living room!
If you cause interference at MHz's which can happen with the modern led driver ic's then place a ferrite bead with the impedance at the correct troubling frequency in series of the power supply to the led.
"power supply to the led" is very ambiguous, and I think the spectrum analyzer might be a bit OTT.