Do I need a Schottky diode as a flyback diode with PWM @ 30 kHz?

I use a regular diode (1N4007) as a flyback diode for a 250 mA5 V fan. My transistor is a 2N 3904 and the PWM generator is an ATtiny85:

I use this one because originally I was switching the PWM signal at low frequency (< 1000 Hz).

I was able to ear a high pitch noise because the PWM signal was in the audible range. I decided to raise the PWM signal to 30 kHz. It seems to be working fine, I don't have a good scope to see the signal and most importantly, I can't hear the high pitch switching sound anymore.

But after watching the video from afrotechmods (https://www.youtube.com/watch?v=LXGtE3X2k7Y) he says that we need a Schottky diode when we are switching at > 1 kHz.

Should I de-solder my diode and replace it with a 1N 5817?