What have we got here?
Hey there. It looks like you have an operator similar to the 39-220B. The opposite-handed version is the 39-221B. At first I'd say, check out the 39-376 and 39-452 handle and cover kits and see which style you prefer (their opposite-handed versions are the 39-375 and 49-451, respectively). The issue is that with some of the older versions of these operator, the cover is not removable. If that's the case with yours, you might be able to just replace the handle with a folding handle instead like the 39-205, or a T handle like the 39-102. Take a look at these options and see what you think.
The 39-205 folds at the base. It can be raised up for cranking the window, and then lowered back down against the operator body when not in use. If there's no way for the cover to snap off your old assembly then likely it is riveted on, and yes, you'd need to replace the entire operator to use a new folding handle and cover kit. Let me know if you have further questions.
See if the 39-220B matches your old operator.