Domai.nr links to GoDaddy too. So much for you saying, I'll never use your service not just because you deal with GoDaddy, but because you even considered dealing with GoDaddy. Never.
Trust me, I don't like GoDaddy either. But they're the most popular registrar, and I think it'd be foolish of me not include them. The market much, much larger than the subset of people like us.
Despite the vitriol for GoDaddy, I understand why you feel the need to include them. Don't let haters (no matter how justified their feelings) stop you from doing what you need to get a business off the ground.
If you don't like GoDaddy it would be nice for you to use your service to also educate users on which registar to use. By making GoDaddy the default, you give it your approval. What might be helpful is a page explaining the registrars, or simply selecting your favorite. No reason for GoDaddy to be the default if even you don't use them.
coffeeprick.com coffeehymen.com coffeemucus.com
...and more! At the very least, it does come up with some unorthodox names that might work out well if you want people to remember your site.