I disassembled the headphones, leaving a long wire on the left one and a short wire on the right. I drilled a 1/8" hole in the top of each earmuff and routed the long left wire out of the left cup, through the headband, and into the right cup. I used the grommets that were already on each wire to make a snug fit. There's just enough slack for the headphones to swivel.
Routing the right speaker wire was much easier because it never leaves the earmuff.
The headphone speakers just sit inside each cup. At first, I tried taking the speaker completely out of its hard shell and resting it in the foam of the hearing protector cups. That didn't work: they were WAY too quiet. I had to put the hard backings on each speaker to hear them.
I wanted to be able to use these as regular, non-headphone hearing protectors too, so I put in a port instead of having a wire dangling there all the time. I soldered the wires to a panel mount headphone jack and wrapped it all in heat shrink. The headphone jack approach is useful because if the wire catches on something, it just pops out instead of breaking the wire (or pulling me head-first into whatever power tool I was using at the time).
In the right earmuff, I had to drill a hole for the jack. Then I had to drill a countersink about halfway through the earmuff because the threaded part of the jack wasn't deep enough to reach all the way through. It was a pain to do, but I'm pretty happy that it came out flush mounted when I was done. It's a nice touch I wouldn't have bothered with if the jack had been longer.
Now I can plug in any 3.5mm audio cable. I got one from Amazon with a right angle at one end so it's not pointed straight down at my shoulder.
Of course, I could have just bought a pair ready-made. Amazon has a pair of Howard Leight Noise-Blocking Stereo Earmuffs. It looks like I actually would have spent less that way, but where's the fun in that?