Yes, a "low head" socket head screw works reasonably well, just counterbore the jaw with an endmill. I'm assuming you'll be making new soft-jaws here.
If the project is trying to refit the existing hard jaws then its going to be a lathe project as suggested, imo. Slitting saw or a hacksaw blade (!) carefully used to make the screwdriving slot. Could also use a dremel tool and its mini cutoff wheel if your hands are steady.
