Would a Surefire L1 Cree and Classic L2 bezel swap be safe?

I have looked around, but have been unable to find out if this is something safe to do. I've lurked this forum for a while to get information before flashlight purchases, and just to generally geek out.

However, I haven't found anybody commenting directly on the safety of swapping the bezels of an L1 cree and an L2 classic (luxeon, throwy). My L1 cree is delightful, and I have, on occasion, put the L1 Cree bezel on the L2, but only for moments at a time, because I'm scared it will be overdriven and hurt the LED. I am pretty sure that both bezels are unprotected/direct drive, though I'm not sure what the differences in drive are like. They both have their important electronics somewhere in the body or tailcap, don't they?

Here is the important question: Is it safe to put the L1 Cree bezel onto the L2 classic body and run it? Will that damage or destroy the L1's LED?

I'm not too versed on the voltages/currents that are safe for either of the LED's in those bezels. I am assuming they have different safe voltages and currents, and may be incompatible, though I hope not, for the frankenstein's superlight that could result. Could some expert and knowledgeable CPFer answer my Ultimate Question?

I'm afraid of the answer, because I want to keep that monstrous output and two stagedness!