I believe it's all got to do with flow, and thus the diametre of your pipes. I believe with 'power shower', you mean one of those 'raindance showers'? If yes, then it's like so that those kind of showers require pipes with larger diametres than come standard in houses (in Belgium this is 16mm, a raindance shower needs at least 22 mm), otherwise the flow is too limited and you'll never have a good shower experience.

An electric shower should work, since as you say it's only connected to the cold water pipe and completely bypasses the boiler. But again, here also applies: if your pipes are not wide enough, the flow is too limited, hence and electric shower also wouldn't work (well). Also take into account that, if the piping in your house is more than 10 years old, the inner diametre of a pipe becomes even smaller because the water continously adds layers of calcium to it (unless you've installed a water softener of course, which I would highly recommend!).