bmx sprocket on a worksman?

It should fit your Workman's crank just fine. However, you might have to use a thicker or thinner space washer under your right side bearing cone depending on clearance. I've used them in the past and didn't have any that I couldn't get to work. I've always used a standard 1/2 X 1/8 chain with them.

one piece cranks are universal. (at least now they are. i have some from the 1930's that are different.)

any sprocket will fit any crank. like mentioned above, you might need to use the washer to get your chain-line straight.