Most of us use some sort of razor. The difference is that some of us use men's razors, and others use women's razors. However, don't all razors essentially perform the same function? I understand that many women's razors come with the cream/lotion already on it for convenience when using it to shave, but that's really the only difference when compared to a men's razor. Razors and other hygiene products (deodorant) are marketed for the different genders, therefore sexing the product. One would think that a neutral tool used for the shaving of hair would not be given a gender code, but marketers think otherwise. The most shocking part of this is that it works! People don't even realize that this is happening.
While you certainly have a point, in that often, similar products are arbitrarily marketed towards women and men differently, I'm not sure if it is always applicable to razors. The vast majority of men who use razors are using them almost exclusively for shaving facial hair. This is likely the case because of socially constructed notions of gender, in which men are as likely to be expected to not shave their legs, underarms, and other areas. Meanwhile, women are far more commonly expected to shave these areas in addition to facial hair, for the same socially constructed reasons.
The point is, that because the razors are generally used for different functions based on one's own expression of gender, it isn't entirely arbitrary to market different types of razors by gender, in the same way the deodorant is marketed.