I guess my only concern with that is that one end would not have barb/lip on it. Are you thinking it will seal fine with just hose clamps even with no barb/lip on one side?
Mine did. When I installed the transmission cooler I had to reconfigure the lines from the transmission to the stock cooler, in the bottom of the radiator, and the new cooler. There was no way that the existing lines would service the additional cooler. I used barbed fitting where possible, but one of the existing lines offered no other possibility than to slip a hose on and clamp it down. The hard lines on my truck, the '92, do not, and never have, go all the way to the cooler. I guess Ford put some hose in the system to combat movement and vibration.
If you feel more comfortable, double clamp, use two hose clamps. This is not a particularly high pressure system.
That being said, have to looked at the connections to the stock cooler at the bottom of the radiator? Are they hard lines all the way to the cooler? Are they hoses going onto barbed connections? Mine are hoses slipped onto what
might be barbed connections. I have hose clamps at the ends of all hoses.