I can attest to the
oil cooler not being needed. I am in the middle of installing an Improved racing sandwich type thermostat to get the
oil temp up. As far as the routing of the lines, that would depend on the type of remote you have. If it's a Canton, it's pretty simple. Canton has an in and out on both sides of the remote.
Oil line out from the engine to the in on the canton. Out of the Canton to the cooler. Through the cooler and back to the engine. Be certain to identify the out line from the engine.
Fred