GoMayoGo: You claim under YOUR policy. If you report under WIFE's policy, you will be asked in any case if you have a policy in your own name with Driving Other Car extension (DOC). You MUST answer truthfully and then they will follow up with your insurers in any case. It will be YOUR NCB that will be affected at next renewal.
If you tell a lie and say you do not have DOC and they find out that you do and that you told a lie, they they could seek to avoid paying out, the claim, or if they do pay out, will seek recovery from you. That would have far more serious implications for you both at next renewal date, especially if they thought that you were perpetrating a FRAUD.