Okay I finally managed to get it fixed (ish). Please keep in mind, I know very little of what I am doing, so I wouldn't suggest using this as a guide per se. Like Ian said, any two core wire will do. Based on this post, I found the wire thickness to be 15 gauge total, with the internal wires being 27 gauge each. I couldn't find a dual core wire with the same thickness so ended up buying these, 30 awg wires (I would advice buying two colors to keep track of +/-). IMPORTANTLY, after the fix, the speakers are working great, but I can't adjust the headband any longer. This has to do with the fact I bought two separate wires, and they dislodge themselves in the headphone, getting stuck in the adjustment mechanism. Additionally I have, sometimes, some interference in the headphone (sounds like the noise speakers used to make when getting a text).
Opening the headphones is pretty straight forward, everything is held in place by small torx like screws. Do take pictures of everything along the way to make sure how it was assembled, especially the electronics. I used this guide as a reference for taking apart (do note, if you just want to replace the wire between the speakers, you don't have to follow every step in the guide).
Important things to take pictures of:
Controller board slot in one of the earpieces:

and the wiring on that same board:

direction of wiring on the two speakers:

I first ran the new wires through the back of the headphone, everything should come apart, so you have easy access the replace the broken wire:


This is where my wires kept dislodging and getting stuck in the adjustment mechanism:

I then resoldered the new wires to the speakers, and the small controller board in the same +/- order as they were in. Reassembled the headphone and tested it.
Overall the headphones have been working great for the past 2 ish weeks with almost entire day usage. The only two problems with this fix are the lack of adjustment after re-assembly and the occasional (maybe once every two days for a couple seconds) interference.
Hope this can help anyone else, and do let me know if you have any questions.