you could probarly use the outside socket prociding you got aplug in rcd but thats nor realy proper power you wouldn't have to notify anyone if you done that as it is classed an non fixed wireing its jsut like a big trailling lead but its not the way i would d do it to do it properly is a big...
it is fine to mount the cable in trunking but you must have another isolation switch near the shower but you must no be able to operate once on the shower for obvius reasons the low flow your are haveing trouble with may ce from insuficient mains pressure check the shower is not fed by a 10mm...