I don't know about Macs, but in the Win world, you can take a PKL (portable keyboard layout) with you on a flash drive. It doesn't require installation and runs memory res, so you don't need admin rights. I use Colemak myself, but Dvorak would be the same. Further, when I'm running Colemak, when I use VMware or Hyper-V, no issues for me. My layout is implemented on the remote systems.
You might look for a Mac Dvorak PKL that you could take with you to client systems. TKL layout makes no difference in this case. It's just a matter of the keyboard layout you're using.
If that doesn't work in the Crapintosh world, I don't know what to tell you. Maybe ask the almighty Apple if something like that has been sanctioned by Steve Jobs. Sorry if I come across negative. It's just I prefer to be able to make those choices without the required approval of the Almighty Apple. Hence, the name Macsmasher lol.
The other option would be to buy a keyboard with a dip switch for Dvorak. Since that's at the hardware level, the OS doesn't have to do anything.