First, I'm not sure that would not still be classed as a device with a built in (non user serviceable) battery?
Second, is it dead or just not lasting as long as before, if it is dead you can't break it any more than it is. Is it screwed together or does it just have that horrible plastic melted together case, if it is screwed together, get the screwdriver and camera and be the first to document changing the battery!
I have always believed if man made it I can try
to fix it, may not be successful, especially if it is plastic welded together.
Good luck finding the solution.
Sorry no idea on fixing the lights, but just looked up shipping an item with a built in li battery, it seems that there are strict regulations that need to be met but don't look too difficult to adhere to, max weight or ah rating of the battery etc, I don't know if your lights have bigger batteries than the basic limits, but there are provisions for exceeding the basic limit with the correct documentation and declaration.
I suggest having a look under IATA PI-965, I think this is what would cover your situation. It looks like you should be OK to send them.
Thanks Graham, the PCB Vagabond Mini Lithium is a stand-alone external battery pack specced to power Alien Bees, White Lightning and Einstein flash heads comprised of an inverter and removable battery pack.
7DII+Grip, 7D+Grip, 40D+Grip, 5D+Grip, EF 24-105 f4L EF-S 17-85, EF-S 10-22, EF 70-200 f2.8 L IS II, EF 2x III, Σ150-500, Σ17-70 f2.8-4 C, EF 50mm f1.8, 550EX, Triopo TR-985, Godox FC-16, Filters Remotes Macro tubes Tripod heads etc!
5D, 20D, 24-105, BG-E4, BG-E2N, 17-85, Nifty 50 pre owned. 😀