Silicone oil is everywhere available.
the crank case oil could be a bit more specialized.
there are unlimited discussions about crank case oil for compressors in general in every airgun forum.
if i would own this rather expensive hill compressor i would stick to the hill crank case oil
if no more available i would gonna use ISO / VDL 100 Compressor Oil
im using this for about 3 years now in my china yong heng compressor with zero issues
ISO / VDL 100 compressor oil is also used in very big and expensive industrial compressors. they can have the size of a small apartment and they are pricey.