Replace AWS Cognito App Client ID during OAuth2

Question

I need to show custom Client ID in URL during OAuth2 authorization flow according to regulation docs.

Path e.g.: https://test.auth.eu-west-1.amazoncognito.com/oauth2/authorize?response_type=code&client_id=CUSTOM_ID

How can I do it? Any hacks, ideas?

I think about redirecting to this link of Cognito in my internal API with mapping CUSTOM_ID:AUTO-GENERATED CLIENT_ID.

But it sounds weird...