I have a 2004 Terrimite, T5C, backhoe. It has a TRW hydrostatic motor. Don't know what the pump uses. In big bold letters, it says use 10w40 or 10w30 only. DO NOT USE HYDRAULIC OIL, IT WILL CAUSE DAMAGE. There is only one pump for everything, the motor and all the cylinders.
I would try to contact the place that made your skidder.