My girlfriend was adopted and it’s a conversation we have every few months. At the moment she has decided to leave it as her parents have done so much for her, and inevitably would cause some upset to them, even if she does have their full support doing this.
In your situation, I can’t see you have anything to lose. As you’re not a direct relative requiring any type of support to your potential family members, you won’t be a burden a such, therefore much more likely to be accepted into any existing family environment.
Worst situation is either you find nothing, or your fathers blood family don’t want any contact. Either way, you don’t lose out and at least have an answer.
Keep us updated anyway as the missus would be interested to hear the outcome.