If you decide to use the external cooler only install a good, accurate, tranny temp gauge in the pan so you know what the actual trans fluid temps are
If it never gets above 160 F move it to a place that it will run from 160 to 240 F all the time
Dominic,Thumperdart, did what you doing when he went to a aluminum radiator in his BB Dart, he had a small three row cooler mounted in front of the radiator and the trans temps in the summer in Victorville, CA in the Mohave desert never got above 140 F when he was beating on the car street racing it in town
He moved so it was between the bumper and the radiator mounted horizontal to the street out of the main air flow and it ran from 160 to 220 F