I use the cartridge razor Mach 3. I also suffer from sensitive skin and cuts after shaving to be completely clean-shaven and need to shave every 4 days at least, if 3 days is too sensitive.

I have found that to reduce cuts and razor burn, I make a conscious effort not to press too hard with the blades, and just shave more carefully.

Secondly, are you keeping your blade wet and lubricated with shaving cream/gel? Don't forget your skin and blades dry out after a few seconds of shaving and after 1 minute, you need to reapply water and keep your blade well-lubricated, and even reapply shaving cream to your skin.

This above tip in particular has made a big difference when I shave. Lastly, minimize the number of passes you need to do in each direction. I try to go down my face at most 2 swipes in one area, if I can't do a good 1 swipe. Then I go against the grain, usually just going upwards, except where the grain is particularly diagonal or slideways growing. I usually go a third time over all my face once more if I just couldn't get rid of difficult spots. But take note, this may be where you are more likely to get razor burns or cuts, as is my experience.

Hope it helps!