Sprocket

Can we tap and die the sproket on the out drive shaft so as to hold the sproket in place?

A lot depends on your set up, however, I would try to find another method (welding, cutting a key, pinning…). One of the most probable problems would be the sprocket “unscrewing” itself from the shaft depending on the direction of rotation.

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Sounds iffy to me, why not try set screws?

To Quote Woodie Flowers “Setscrews inhale audibly.” :ahh:

Can you legally? Yes. Should you? Maybe not. Using threads is not the best way to transmit torque. At the least, you would also need a left-handed threaded hole int he end of the shaft in which you place a retaining bolt and washer, like how a drill chuck is held on.