Changing the context of a custom field in an existing project is expected to have the ability cause data loss on that field. I would recommend taking a look at Change Context for an Existing Custom Field Without Losing Old Data.
That KB explains how you can create an entirely new context for the same custom field to use in a new different project. That does work for creating a new context for the custom field However from your request it sounds like you want to change the context for this existing project.
I think you would need to find a way to backup/copy that data in those fields before you make this context change. That KB does have a set of steps where you can search for issues that have each specific value in that custom field context, from there you can then use the bulk change in JIRA in order to update another custom field that is setup with the same settings as the old custom field context. From that point it could be feasible to keep that custom field data duplicated in this new temp field for now.
The problem I see with this method is that if your existing context has a lot of different options, these steps will take a very long time to complete as you have to repeat this search/bulk update for each option in the list. If you only have about 5 or less it's certainly managable, but if the custom field say has 20 or more options, it becomes tedious to do this manually.
I would also recommend Establishing Staging Server Environments for JIRA - Atlassian Documentation in order to test out this kind of change so that you can test this on a backup instance before trying this change in a production environment.
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