For me, I am running a remote oil filter (i didnt like how close the filter was to the headers) but I havent mounted a oil cooler on mine yet, (it has not needed it yet, but i have only had it in the cold).
But if i did it would be easy, just run in line with the remote oil filter.
There are kits for oil coolers, that mount a adpter between the filter and the mount, but space is the issue with those.
Also check your trans temps, I have heard from a few guys over the years that had heat issues with a 403 but only under heavy loads (towing, etc.), they found out there trans's where running hot, and in turn heated the motor thru direct heat tranfer (trans case to engine block), and by heating the coolant in the radiator (from the trans cooler in the radiator).
As for my radiator, i am running the stock "Heavy duty" aluminum replacment for a a cutlass with a 307 from my local auto parts store. its a 2 row, with decent size rows.
1987 Cutlass Supreme, with an olds. 403, punched out .040", Deck & heads milled .010" each, Crane fireball cam, edelbrock intake & 750cfm carb, th350 trans, w/ higher stall torgue converter (approx. 1000rpm over stock stall speed). And a 2.14 rear gear. (yes I said 2.14)