^ ^ FDL isn't considered in this matchup since it's a game-breaker and nulls his other masks.
Anyway, I have a hard time understanding why people claim WW Link is no more agile than the other Links. For one thing, his roll parry is a ridiculously fast move, and all his neutral combo attacks carry him all over the place. While TP Link has a lot of finesse with the sword, WW Link can pull off a bunch of his moves both faster, more reliably, and while keeping himself moving out of danger. Just jump into one of those rooms of death on the islands and you'll see what I'm talking about. WW Link has been shown to be exceptionally able to defend himself in a melee, which is kind of what we're talking about here.
"Experience" is a subjective term, since objective evidence of skill beats supposed experiences. TP Link doesn't really have anything the other Links don't in terms of swordsmanship until the Hero's Shade teaches it to him.
You also shouldn't be so quick to disregard Brawl as a source here- while it doesn't take as much into account, you'll notice that WW Link is both higher up in tiers, and that his aerial moves (except for the up/downstabs) are actually taken from his attack animations in WW, whereas TP Link remains a ground-focused character who is forced to play defensively- much like in his actual game (while his aerial moves are almost entirely fabricated). Conversely, in both WW and Brawl, it's obvious that WW Link has much more mobility and offensive prowess. In a melee like what's described here, TP Link is going to have significant difficulty coping with attacks from all sides, whereas WW Link has experience with this type of fight.
What I'm saying is that in these conditions, where a host of Links are attacking from all sides, WW Link is best equipped to deal with the situation. It's totally obvious that in a duel between TP Link and WW Link, TP would come out on top due to a more varied and powerful aresenal for this type of fight. However, in a melee, TP Link, while more powerful than almost any handheld Link (except for maybe Aol's magic and FS/A's teamups), is going to have trouble defending himself from all sides- rarely a problem for WW.