Nothing really has to be said at that point. Your dad can just greet your almost-spouse, maybe hug, maybe just a handshake, and then your dad can turn to you, give you a hug and kiss, and pass your hand to your almost-husband, and go have a seat.
In our wedding I tried to stay away from too much of the 'women are chattel to be given by the dad to the husband' imagery. In fact, we borrowed from Jewish tradition - my husband's mom and dad walked him down the aisle and left him standing up at the front, then my mom and dad walked me up the aisle to meet him. That way it was both parents, both families giving and receiving.
Good luck with all your wedding planning!