To my knowledge, the oil is not affected in this application. The life of the oil is too short, 50-100h max compared to a hydraulic system (several thousands of hours). The most likely component(s) to cause cavitation (vapour) are also not oil components but fuel! When my oil temps wouldn't come up to 80-90deg C, I had over 2% of fuel dilution in the oil (most of the time it is under 1%).
Cavitation is caused by a small part of the fluid experiencing a local pressure that is below the vapour point eg forming a tiny vapour bubble. Speeding up a pump that already struggles to get enough fluid supplied is not the fix. The usual remedy is the reduce the suction loss (reduce pipe length, increase dia and replace/remove fittings with low-loss versions). If that is not possible, increase the source pressure (elevated reservoir or pressurising it).
I have a Tecnam P92 and Tecnam, in their wisdom, is installing the oil cooler with the inlet/outlet fittings down (contrary to Rotax installation requirement). After every oil change, I'm cranking the engine with spark plugs removed until I have steady oil pressure. When cleaning out the tank, I also drain the lines and then use a vacuum pump (oil sample pump) to bleed the suction lines and oil cooler at the oil pump inlet.