The best you can do is remove the bottom fitting where the line attaches to the cooler and let it drain. That would be pretty messy IMO. I just change it per normal. What you have left in the system is about 3/4 a quart that is in the lower line and the radiator. I just risk it as it is mixing with 7 1/4 fresh qts of synthetic Mobil 1.
If I was thinking I would have put a quick disconnect in the lines where they go by the sway bar area. I think DMTNT used something like this for his rear trans cooler set-up. This way you could disconnect the lines like an air hose and it would drain both lines and the radiator. Wonder why I didn't think of that before I installed it. Now I have to check, I think I have enough slack to add it.