At 32kHz you need to be wary of switching losses and EMI. For the higher switching frequencies GaNFETs
are the way to go, although they are harder to work with (very fine pin pitch surface mount packages,
special driver ICs needed, significant gate leakage current).
No gate resistor is fine, just choose a gate driver with the appropriate output resistance for the current
you need for fast-enough switching. With 32kHz you have 15us on average between switching events,
so the switching should be a tiny fraction of that, like 1%, so 150ns switching time is a starting point.
Calculate the current from the switching time and the total gate charge:
I = gate charge (C) / switching time (s), so 62nC / 1.5e-7 = 400mA