dexron III has all the properties of the dexron II... and will work in its place. when the manual was printed, dexII was still a popular oil, but not so much anymore
If you want to get specific, the ISO 22 designation is regular hydraulic oil without additives used for filling hydraulic jacks... sometimes seen on the shelves of the autoparts stores labeled as jack oil or hydraulic jack oil. its thinner than ISO 32 or 46, which is what is normally used as hydraulic oil in large equipment.
but a LOT of the equipment manufactures are going to the dexIII as its a thinner and better oil so it flows thru the system of small orifaces with less resistance.
Dex4 and type F are different oils, so I would stay away form those except in extreme conditions when any type of oil is better than no oil at all, but I would use the dex III without any hesitation or reservation.