I think it will, I seem to recall that the fork centres on the S'dream, RS and CX500* are all the same, as indeed are the fork diameters and, possibly, the steering stem heights.
I think the 400/4 stuff also fits. It's a shame I've just sold all my 400/4 bits

Does your K4 have 33mm forks? If so then it may be that you can just slot a 'dream front end straight in to your yokes (stranger things have happened).
GC
* a good bodge 'back in the day' was to throw away that nasty steel plate top yoke from the 'Dream and fit a cast aluminium one from a CX. Stiffened the whole thing up a treat.