Well, with caveat that the term "correct" is a reach in this situation, i think a 5/8 barb will work.

Just be sure you are comfy with this - you are going to cut both of the rubber lines about 10 inches or so before the factory cooler, splice in with a coupla adapters you preassy from the hardware store, use some higher end hose clamps, and add your aftermarket cooler of choice to the path. Pay attention to which hose is in, and which is out. Have the fluid go through the factory cooler, then your add on cooler.

Have clamping pliers handy to pinch off the factory hoses before you cut or you will be laying in a puddle with fluid dripping in your eye the whole time.

I personally don't find anything sacred in a 12 yr old car, but this kind of thing can make some folks a little concerned. Just so you know you are basically forging the path that seems right to you, under the car, with oil dripping in your eye. This isn't a well traveled road.