Remember that yellow represents fear now though. It only works as a weakness theoretically if one has fear of anything. Green K would still hurt Clark even with the ring.
Couldn't he have the ring block the radiation of Kryptonite, of any color, and keep it from hurting him?
I guess so. Old-style Green Lanterns were not completely powerless in the presence of a blackbody radiator like the sun, so just because some object that's radioactive is yellow should have had no effect.
Another weird thing is that kryptonite was sometimes used as a power source, but it's always been depicted as either completely innocuous or with only long-term health effects. I don't think a radioactive material could be both.