I like Mandar's suggestion to use a form processing step - Include 2 form processing steps for sending email notifications:
- Configure one to send the payment information based on the condition that the value selected for the response field = "No"
- Configure the other to send the "thanks for registering" email based on the condition that the value selected for the response field = "Yes"
Then use a filter/segment/report to identify which Contacts received each email.
I hope that helps!