Hon, it's kinda built into us to need parental approval and the waiting game is a quiet torture all of its own. I'd love to say for certain that it's going to be ok, and I suspect if your sister has anything to do with it, you'll be fine.
Personally, you've had years to get used to the idea, your sister has had weeks, and your dad has days.
Maybe for him, there will be the struggles of 'what ifs' for the son he never had, he will be mourning the loss of that potential future, where with rose tints he imagined a completely different outcome - but one thing is for certain, he's going to need some time. He may have already reached out to your sister, and it's probably worth talking with her about it, he may simply be trying to research, understand and then be able to express himself in a way that is ok that he still loves you and supports you, even if right now he doesn't understand it.
(Hugs)
Rowan