Ah, I love it when cosplayers worry about details that almost no one else is ever going to remotely care about. God knows I do this, unashamedly. Woefully, I'm presently too lazy to inspect the ref photos enough to weigh in on the symmetry matter.
The wooden core looks nice and secure. That should help a good deal.
I think you might want to go back to the ref photos and take some measurements to get it a bit closer. You can either use image software to get measurements or a vernier or dial caliper (if you don't own either, even a cheap Harbor Freight one is a good investment). You work out some ratio that you can be sure of, such as the length of the hilt times the fraction covered by the character's hand compared to the length of your hand, and then you scale everything up by that ratio, keeping accounting for the concept of vanishing point in 2D drawings in mind.
Going by the reference, it looks like the blade should be less wide, and the taper between the widest part of the blade and the thinnest part of the blade should be less significant. It's a very subtle taper. Almost a straight blade.
Naturally, if you're actively choosing to go against ref photos to accentuate certain details, that's up to you as the artist, and there's nothing wrong with that.