I have a splitter just like that, it just has a different brand name. I use regular Supertech R&O Hydraulic Fluid. Works just fine. Any Rust & Oxidation hydraulic oil should be fine. I saw something similar at Tractor Supply Company. Try any farm oriented retailer.
Also, make sure you loosen the wing nut by the splitter prior to use. It needs to be open to work properly. Otherwise, you will push fluid past the seals, possibly damaging them. At best, you will leak oil. Ask me how I learned this...
The wing nut only needs to be closed for transport.