How to rename an area when multiple areas have the same name?

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I need to rename an area on a single page but the problem is that there is another area with the same name on a page type.

I need to rename it because, I use a PHP function working on area names.

Using the following request :
SELECT TABLE_NAME FROM information_schema.columns WHERE table_schema = 'concrete5' AND COLUMN_NAME = 'arHandle'


I know that the list of table to modify is:
AreaPermissionAssignments
Areas
CollectionVersionAreaStyles
CollectionVersionBlockStyles
CollectionVersionBlocks
CollectionVersionBlocksOutputCache
PageTypeComposerOutputBlocks


But the problem is that I can't use requests such as
UPDATE Areas SET arHandle = 'OldName' WHERE arHandle = 'NewName';

( as proposed in https://www.concrete5.org/community/forums/customizing_c5/how-to-ren... )
because some OldName arHandle are related to the single page and some OldName arHandle are related to the page type. And I want to modify the area name only on the single page.

Of course, the site is in production and users have already put a lot of content.

Any ideas?