I've never really thought Link had any kind of blood connection to any member of the Hylian Royal Family and even though Skyward Sword leaves little reason to think Link wasn't the first King or whatever, it doesn't mean he was. After all, going to the wild lands of The Surface and founding a kingdom wouldn't just happen in a matter of months. It seems possible to me that Hyrule as a nation may have only been established after the death of Skyward Sword's Link and Zelda and that Zelda's descendants were the first Royals. After Link spent so much time saving the Kikwi's, helping the Mogmas and Parellas and assisting the Dragons, I find it hard to imagine he would then go and tell them all he's in charge now.
Yes, it does appear that Zelda and Link are in love in Skyward Sword but in order to found Hyrule, more of the citizens of Skyloft would have had to go to The Surface. If Gaepora went down, would he have become King? He certainly resembles the kings from the other games and is obviously part of Zelda's bloodline. What if Link had to go off on some other adventure and in his absence, Zelda fell in love with someone else?
I don't know, I'm just throwing stuff out there but, anyway, I don't think any of the Link's are related to the Royal Family by blood.