I just re-watched the scene on the "Widescreen Limited Edition" version of A New Hope. This is the one that contained not only the re-mastered and Lucas-ized update done in 2006, but also a copy of the earlier print that was not restored. (And you can see a lot of clarity and picture stability issues in it.)
In that print, Luke throws the line and hook, it hooks, and he pulls on it, and Leia kisses him before they swing across. That's how I remember it from 1977 onwards, at least the kiss. (That she gives him a kiss before they swing across.)
However, this is the version that had the echo added to the dialogue between Luke and Leia, so it had already been altered from the original 1977 version of Star Wars. I know this echo was added for an early re-release that was before 1981. (I won't go into the landmarks of my life, but let's just say I know it was out before 1981, and likely before 1980, when The Empire Strikes Back came out.) That means, with this print, which is the earliest available (remastering was done later, after the echo was added), we can only go back to around 1980 at the earliest.
For what it's worth, I have always been puzzled by that, as well. I thought I remembered Luke throwing the line once, it not catching, and having to throw it again, but it's not in this print. (I am positive, though, that the kiss was always just before they swung across the line -- trust me, you see a movie like this as a teen on a date with a girl you've been drooling over for a few months, you remember every kissing scene in the movie!)
So if it did exist, it was cut before 1980 or 1981 and it's going to be almost impossible to find any version of the film to back up that it was once there.