The PSU is stock, in fact, I envy you for having an ILT head and PSU that are in such amazing condition!
Especially given the fact that you have the water cooled 1,5W version on single phase, this one is beyond unique. Not even a scratch on the casings, circuit boards look brand new without a speck of dust. I'd hold on to this puppy if I were you -- you're looking at a priceless collector's piece.
It's almost a shame to sabotage the medical circuitry on the head to allow it to operate CW since it would compromise its original condition. Steve: Is there a way the board can be disconnected with some degree of elegance so the (internal and external) cosmetic condition of this beauty won't be violated?
If I were to play on a hunch, I would defeat the entire operator interface on the PSU connection end. The PSU itself doesn't know about the fact that there's a medical laser on the other end, it just notices the interlock is broken after a few seconds of run-time, caused by the operator interface board. So defeating that (and only leaving the case interlock intact) would make it run CW.
You'd have to be careful and sure if the PSU can supply enough current to the laser all of the time though. 1,5W is a lot of power and you'd need quite a lot of juice to keep that up.