I too have sensitive skin and I get allergic when I wax. I shave my legs too. I follow this procedure to avoid any discomfort while shaving.
1. I use sharp use-and-throw razors, I use each one for a week.
2. First, I shower and use in-shower moisturizing lotion afterwards. At the end I use the razor to quickly shave my legs while my skin pores are still open due to heat.
3. I shave in the direction of hair-growth. Experts do not advise to shave upwards or in the opposite direction of hair growth as it interferes with the direction of hair.
4. After shaving, I wash off with cold water and then use little bit of lotion after drying.
5. Every other day I use a body scrub to avoid ingrown hair.
Hope this information helps.