What type of squeegee should I use when oiling a floor?
It's the type of rubber you use for the blade.

Neoprene or Viton will not dissolve in oil. We used a heavier form of Neoprene squeegee for cleanup after mopping the garage floor to remove oil and grease in our automotive shop. Squeegee'd floors dry a lot quicker.

It's necessary to use an oil resistant synthetic rubber compound for the squeegee blade in this instance, especially if this substance has mineral oil or paint thinner as an additive. Petroleum and natural rubbers don't mix.

So window squeegees which often are natural rubber or a mix of synthetic and natural rubber are definitely out. They work extremely well on windows, just not for situations where oils are present.