I never use razors designed for women, I use Schick for Men razors. The Titanium Quattro.
We bought both the Women's Schick Quattro and the Men's Schick Quattro razor packages with the handle and the blade. I kept my handle and ditched the blades for the women's version because I hated the blades but loved the handle (it's lighter than the one for men and has more rubber grips on the handle).
My skin is never irritated and I very rarely nick my knees. I also use regular, unscented, dye-free hair conditioner (Suave) as shaving cream. It's thicker, stays in place and you can see the skin better and inexpensive.
Shaving creams/gels have alcohol in them and that might be the true cause of the irritation plus the dyes and perfumes can be irritating to freshly shaved skin. Try using conditioner and let it sit on the area you wish to shave for a few minutes before you begin and see if you notice a difference afterwards.