I didn't bother because you just said you haven't even learned BJD, in any style, never mind WC. So, it is pointless to do a comparison with you.
That is actually the biggest cop out I have seen you ever make and it contradicts your premise. Your claim was that only the empty hand portion of WC/VT is unique, that the use of twin knives is not, ergo the Baat Jaam Do section is predates the empty hand.
If the BJD section predates WC then you would not need actual BJD training to see the truth of what you say and simply extensive sword/knife experience.
You do not need to be an trained in a specific martial art's techniques in order to see the biomechanical differences in techniques between different arts when it comes to weapons. You simply need to understand how those weapons/tools work. So you have (apologies for the quality of the first video)
or
and then
or
first note, especially in the last video, the swords/knives that are clearly designed with stabbing in mind (one of the other things I pointed out.). Additionally a Hung Ga sword/knife tends to be longer than a WC sword/knife, even if by but an inch or two.
Regardless, I do not need to have studied either of these to see the biomechanical differences. If you look at all of the videos, and then the description i wrote that you chose to ignore, you will see that my break down of just a few of the differences is fairly accurate. Why? Because I know how to fight with swords and knives. This knowledge allows me to also see similarities to what I do in both arts. Examples.
Like the WC form we do not go too wide, we keep things close so we can always be defending and attacking simultaneously. We also try to keep a largely "up right" posture without leaning to me efficiently protect the head, among other things. Also, as with the more modern "chopper" Baat Jaam do, most Filipino blades tend to be single edged (some have a short false edge) and are also more suited to chopping, so thrusts are less common than slashing and chopping.
However there are times we will go "deep" or "round" with a technique like they do in Hung Ga, but for a specific purposes and with some key difference. You may want to attack the foot/shin of an opponent because an opponent with a "chopped" foot is going to have issues fighting you. You do this by "sinking" with your legs, without the accompanying strong lean you see in Hung Ga, so you can still defend yourself without offering the opponent your noggin. As for round there are techniques referred to as "redondo" and "abaniko" which are essentially fanning actions but only using the wrist and elbows, not the shoulder. You can do this as an attack or a defensive maneuver.
The point of the last paragraph being that when you know how to use weapons in a variety of ways you can see where other arts have similarities and differences to what you do. To simply dismiss this reality (and it is a reality) and needing to contradict yourself in order to dismiss this, is to be trapped in dogma.