Can noise from contra-rotating propellers be reduced by having a different number of blades on each propeller?
It does help a little, yes.

One source of noise is the fluctuation in dynamic pressure experienced by a blade of the rear propeller when it cuts through the wake of a blade of the forward propeller. Friction in the boundary layer on the first blade will reduce the dynamic pressure locally and create pressure fluctuations on the second blade, and noise.

By using a different number of blades, the pressure fluctuations will not happen all at the same time, but sequentially, which reduces the peak power of the noise. The effect of the second blade cutting through the wake of the first is still there, but is distributed over time.

Thanks to @MSalters for pointing out another effect. I copy straight from his comment:
The effect is not just distributed over time, but also shifted up in frequency. At 6000 RPM (100 Hz), with 4 blades per propeller they pass each other 8 times per revolution (800 Hz). If the second propeller has 5 blades, this moves up to 4000 Hz.



P-27 prop on the D-27 turboshaft of the An-70 transport, picture by Marina Lystseva. The forward propeller has 8 blades and the rear propeller has 6. For optimum noise reduction, the rear propeller should have just one blade less than the forward propeller. The leading edge sweep helps to stretch out the contact of a single blade with the wake over time, which again reduces peak noise.