Adding a stereo input jack to bluetooth headphones

Hello all! Hopefully this hasn't already been posted about, I couldn't find anything using the search.
I recently acquired a pair of OneAudio Studio Wireless M headphones by accident. I got them as an open box for super cheap and didn't realize they were a bluetooth model with no input jack. They were so cheap it wasn't worth shipping them back, and they actually sound decent enough for the price. I figured theyre good for when I'm doing homework and I don't have to worry about breaking them if I toss them in my backpack for school.

That being said, I'd like to add a wired option to them so I can use them if the battery is dead. I've never dealt with bluetooth so I was wondering if you could provide some help. I'm assuming the receiver must have output wires to the drivers that I could solder the jack to. What I'm not sure of is if I need to add some sort of switch to change the source, or if just having the headphones shut off when I plug them in would be sufficient.

I think this should be pretty simple to do, I'm just still learning about how electronics work so I thought I'd ask the pro's. I figure its also a good pair of headphones to play with since they were super cheap and if I mess something up I won't be out much. Thanks in advance!