My Sutherland's Manual states the 12x3/16" balls per side is correct and mentions a "shallow cut cone". My memory matches this and I can say that only the correct cone and balls will work as intended. The cones have a ball track which is only about 2/3 of the cone's "thickness", the axle to outer surface height. (Generally most cones have the ball track cover nearly the entire "thickness").

The manual also states either 9mmx26tpi or 9mmx1mpt as the axle threading likely for a Q/R axle. These two specs are really close to the same pitch but a cone likely will have enough length of thread so the difference likely will be a problem. I suggest a complete Normandy Comp axle set as a first choice for replacement. This is where having an old time service focused shop near by can be a big plus. These days that's often the non profit operation helping those who can't afford other transportation. Andy