The purpose of at least the external portion of the tapered groove pin is to prevent pulling the index pin completely out and eventually getting lost.
If the taper pin is in fact retaining the 0.094" dia. pin, then if you can get the remains of the 0.094" dia. pin out, you could replace it. But Frank gave the groove pin size as 1/8" and they do not have much taper. The slightly larger 10-42A used in the 10" and 12" is one machined piece plus a 1/8" dia. roll pin.