Whoa, hi there, everyone! I was not expecting my notifs to explode. Um, let me just preface this with the following: I am certainly not an expert in any way and am always happy to be educated if I'm wrong, so take this ramble for what it is.
That being said, here's why I personally really like the inclusion of a wakizashi in TLYW music video.
There's a variety of swords that Japan has utilized for a number of purposes throughout history - be it ritualistic, for defense, as a status symbol, and so on - with the word katana probably being what most people think of when the topic comes up. Katana is actually the general word in Japanese for a single-edged sword, whereas the actual blade closest to resembling that word is uchigatana, and it's known for being a double-handed single-edged sword with a longer grip handle to accommodate both hands, often used for fights needing quicker response times like dispatching someone in a single blow. They are differentiated from (and technically originated from, I believe?) tachi, longer blades with a history of cavalry usage before fighting on foot, infantry, because more common, which helped make uchigatanas more widely-wised. Uchigatanas and tachi blades have an interwoven history with one another, as far as how they influenced styles being made, who used them, and so on.
Now with wakizashi blades, they kind of dance in between as far as sizes, ranging anywhere from as long as a katana (reaching up to 2ft/60cm) to being almost as small as another blade (as small as 1ft/30cm), called a tantou. Tantous are small blades typically reaching 1ft/30cm, easy to fit in the sash of a robe, and were used for anything from ceremonial purposes to ritual suicide. Tantous were often being used in as a pairing with tachi blades, having two different options for combat or other uses. This is similar to how people would eventually shift to using uchigatanas for their longer swords and wakizashis for their smaller swords as a pair as history went on, the style of fighting changed, and so on.
The reason I bring these different types up along with their connections to one another is because I want to say it can be easy to question which sword Vessel is using - especially with how tall he is, the scale might be a bit skewed as far as comparing it the length of the blades, not to mention there isn't many great shots of the blade unsheathed and not in use save for when he draws it.
I want to say it's a wakizashi.
Wakizashi blades specifically were used for close-quartered fighting, like if you were indoors or in a narrow area where your larger blade would only get stuck in walls, obstacles, you name it. Fitting with the narrative of the video, with Vessel seemingly repeating this cycle over and over, wakizashis are also used for when the wielder feels like they're at a disadvantage, when they're trying to get close enough to deal a killing blow and live to fight another day. He's clearly done this before based off the sheer numbers of ribbons tied onto the tree at the start and finish of the video, and how the main dancer has the ribbon and is the one to dispatch him. I want to say as well that the blade's grip is small enough for only single-handed usage, especially based on the image here, whereas if Vessel used a uchigatana it'd probably look a little funny considering how he fought.
Wakizashi and tantou blades are unique as well in that they were used for ritualistic suicide, or seppuku - small enough to do the job correctly, so to speak (which for those curious, feel free to read up on how that's done.) Given that he seems to be taken over in the end, it's hard to say how willing Vessel was in that action - if he did it to preserve some honor, to prevent himself from being tormented by the dancers and by Sleep, or if it was just a forced end to repeat the cycle. There's no denying that he's stuck, at a disadvantage that death seems to be the only cure for - regardless of any metaphors found in the lyrics.
Additionally, the overall environment reminds me - (and I preface this with saying I am using this comparison with nothing but respect) - a bit of Aokigahara as well, a forest in Japan known for those passing there by suicide. Sometimes those there will leave markers as a way to add on counters or as a reminder to change their minds while contemplating. (The ribbons also remind me of ceremonial offerings for purification, but that's another ramble and as you can see, I'm probably not as organized I should be with this one.)
But yes, given the blade's size and how Vessel uses it both for fighting and for repeating the cycle, and with how you can relate it to the video's narrative, I really want to say it is a wakizashi blade.
If I can think of anything else I'll be sure to add on, since I didn't really plan this out, and anyone else is welcome to jump in and share what they know (or please correct me if I'm wrong.) But, um, I hope this was interesting, at the very least!
(Tagging @a-s-levynn as your post inspired this, and @thejawsoffate and @moonchild-in-blue for the additional encouragement; hope that's okay! Thanks, too, for everyone interested. It means a lot to me.)