The reason to prefer a CMOS 555 is it has a rail-to-rail output, which the bipolar 555s don't have. This affects the On time and makes it greater than the Off time with your pot centered. Also, you have to allow for the input base bias currents, which result in issues with high value timing resistors. OTOH a bipolar 555 typically has about twice the output drive capability when compared to a CMOS one.
I suggest you try it on a breadboard with the NE555 you have.
N.B. that circuit is UNSUITABLE for high frequency PWM due to the poor turn-on gate drive. If you add a NPN emitter follower between the Discharge pin pullup (make it 1K) and the MOSFET gate, with a Schottky diode b-e, cathode to b, ('poor man's' gate driver for open collector outputs), the turn-on will be much faster and the MOSFET should run cool even if you increase the PWM frequency.