You can just update the SOE. There is no need to unregister/re-register at 10.1. In Manager, on the Extensions page, each .soe file that's listed on the page has an edit icon and a delete icon (cross). Click the edit icon next to your SOE. It will let you browse to the updated .soe file. Please note that the update .soe file must carry the same SOE as before, no more, no less.
Thanks!
Ajit