To do this in SSMS, follow the steps below:

1) Export the system record IDs of the constituents who need the alternate lookup ID type changed.
2) Prepare a script like the following, making changes as directed or otherwise necessary:

set alternatelookupidtypecodeid = '21B679CD-8F2D-4797-B2E7-FA9755193378' -– the ID (GUID) of the alternatelookupIDtypecode you want the constituents to have
where ALTERNATELOOKUPIDTYPECODEID = '47E07EB0-AE95-43A0-ABD6-4C2A5160213A' -- the ID (GUID) of the alternatelookupIDtypecode that you want to change
and constituentid in ('FD0014F9-F8B7-44A3-9B48-0E02A2D52A78',

Paste the exported constituent GUIDs from the csv. To do this easily, highlight the column in the csv containing these values. Right click and click "Format cells". On the Number tab, select Custom. In the "Type:" text book, enter '@'. This will format the values properly so that they can be pasted in the parentheses containing the constituent GUIDs.

3) Be sure to run this in a non-production environment to make sure you get the desired results.