try searching google, im sure the compressor wheel in the k04-001 is slightly smaller than the k03s

not 100% sure though
it does have a larger turbine wheel though..
the reason the oil/coolant/downpipe ect are the same it because it shares the same turbine housing cast as the k03 and the chra housing is the same for the k03 and k04. it starts do differ when you alter the exhaust housing for one like the k04-023 which is for longitudianal cars like the passat.. to fit one to the golf the S3/TT 225 exhaust manifold, oil/coolant lines and downpipe would be needed.
im not sure exactly what tip size is needed for the k04-001.. i would have thought you could get an aftermarket k03s tip to fit to be honest.