You will have to change the complete transmission with another one that includes the OD. I believe the main shaft on the non-OD tranny is quite different from the OD version, so it is not a matter of just adding an OD to back end of your non-OD transmission.
Years ago I did change another 100/6 with a non-OD transmission. It was not difficult and it worked OK. But it is harder today to find a rebuildable 100-6 transmission with an OD.
PS you probably have one of the non-OD Healeys that were built that way from the factory, there were some. I understand these came with a lower numerical rear axle which is a plus whether you make the conversion or not.