I have sensitive skin too & shave at least every other day. I use the Schick Hydro but I use my fiancé's refill blades lol. They're 6 bladed.
I just tried a new razor that I had a coupon for. It has olay moisture bars on the top & bottom of the blades. For the life of me I cannot remember the name of it but its pretty good. Try searching up Olay razor & maybe that'll help lol.