Yes. The reason why a cart (cartridge) razor works so well if that it doesn’t shave very close. A “safety razor” shaves very close. You just have to know how to use one and change blades often. I change the blade about every 3 shaves.
I use a puck of Williams soap with a badger brush and an Israeli razor blade. I don’t cut myself.
My Gillette sensor cartridge lasts me at least a month, and sometimes 6 weeks. Shaves much closer than a single edge.