225 instead of 235 – registration required?

Hello together, I have a few new 225/45 R17 Goodyear UltraGrip Performance 2 in my garage. Mounted on original Audi rims TN 8e0601025as8z8http://www.original-felgen.com/8e0601025as8z8.html Now I would like to drive them on my A4. Since the COC papers only indicate the tyre size 235/45 R17, I have contacted Goodyear if they release the tyres for my car and get the attached document. As I see this is no problem for Goodyear. My Fra ge, do I have to register the tyre size separately with the TÜV? Would that be an individual acceptance, what would that cost me about? Thank you for your help! PS: Incidentally, can recommend the tyre without restriction