I think the technique is far more important than the razor.
For the record, I use Gillette Mach 3, and have verey few problems, and I have the most senstivie skin going - I get a heat rash in a hot bath!
To preprare, run a flannel under the hot water, as hot as you can stand it. Immerse the flannel, and then hold it over the favce, pressing onto the cheeks and under the chin. Repeat and hold as long as you can stand it.
Then lather up with a good 'sensitive' shaving gel and take your time. massange the lather in for at least a minute.
Shave with slow dlownward strokes, rinsing feaquenty in fresh hot water. Do not shave against the direction of growth. Take your time, and let the blade glide, do not press on hard.
Follow this routine and you will have a smooth shave with almost no - if any - cuts.
When you have finished, dab the face with tepid water, and apply moisturiser.
If you want to wear aftershave / cologne, apply it to your forehead and the areas behind your ears - same nice smell, no stinging.
I wouldn;t worry too muchy about these 'battery' wet shaves, the blades cost a fortune, and as i say, it's the technique that makes a good shave.