You could use that hydraulic filter mount and a filter that fits it that is labeled for hydraulic usage in the big filter catalog...Wix, Baldwin, Napa, etc. Don't use just an engine oil filter. This would be a full flow filter on the cooler line.
When you refer to a bypass filter, that would take a very small amount of fluid from the hot side of the cooler line, pass it through an orifice to control flow, through a very dense bypass filter element, and back to the sump. You'll still need the majority of the flow through the cooler.