You can just change the scheme as much as you want. It will mostly not directly affect your data.
If you do something that means data migration is required, then Jira will walk you through that. If, for example, you remove the issue type "Thingy" from the scheme, Jira will look for any issues of type "thingy" in the project and ask you what you want to move them to (e.g. "wotsit". I
There is potential for data loss when you do this - if thingy and wotsit have different configurations, then there are some things that might mean extra migrations
So the answer to the question "how to do it without data loss" is actually "Mostly do nothing, but if you remove an issue type from a scheme, make sure the new issue type has all the fields you want to keep and that its workflow at least has all the same status as the issue type you are going to delete"
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