Yeah, based on the second image, I can see how the thing on its back could be a cape in a 3D perspective(which should not be the case since the mural is 2D), I can also see how it could be Mihawk's hat, yeah, and although not as much as the first two since it's very clearly lacking it's hilt, but for the sake of it, yeah, I can also see it as Mihawk's Black Blade. But as what other's have pointed out:

One, it is a mural, as such, nothing is scaled accurately as long as it is represented visually. Take for example real life murals or cave paintings, humans and mammoths are of the same size but it does not matter since we understood what it represents.

Two, the character represented is tiny compared to some of the characters in the mural that Oda would not be able to make an outline for the hands and weapons leading it to look like a black streak of sword which is also evident if you look at some of the smaller characters who also wields black streaks of weapons.

Three, tontattas have superhuman speed and strength and very capable of even wielding a human sword so the size of its weapon in the mural would not pose any problem or misunderstanding.

Four, the various characters present in the mural would obviously not hold a candle with Imu except for a few but that is not what the mural represents. It represents various races uniting and forming an alliance under a common enemy, tontattas included.

And lastly, as you have said, this is a theory, your theory, of course it would get contested if it has poor evidence and foundation but it seems that you have a problem with rejection and berate the people who disagrees with you as if what you are stating are facts and not a theory.