Versch. Tyre sizes ex factory on the same rim: TÜV registration possible?

The ordered Seat Ateca (equipment “Xcellence”, 2WD) is delivered as 2WD on the factory side with 215/50 R18, at the 4WD with 225/50 R18 (on the same rim, the 4WD has lower track gauge). Since I intend to switch to full-year tyres after delivery, but there are only 225/50 R18, I would have to show this size at the TÜV (COC of the 2WD unfortunately does not include the 225er). Which documents are required for this or takes the TÜV as the basis the factory data and evaluates the Rest “individually”? What costs can be expected?