How do use these through Dvorak? I also use Dvorak although I only type in English and Spanish which are very similar. I make my custom layouts with Autohotkey so they are portable. I also have a page how to do such on Mac and Linux although there not as portable and feature rich as Autohotkey.
I use ibus on Linux, it has an option in the advanced settings to "Use system keyboard layout". This applies the default layout to all other input methods.
Notably Ubuntu comes with Dvorak for Japanese as a default, an option I've never seen anywhere else. So there might be special support for your use case. This solution doesn't scale well though.
My keyboards also both have hardware output to Dvorak, which would probably be the best option on other systems. It's been too long since I've used other systems to have a better answer than that though.
From a brief search, hardware transformers do exist, but they seem excessively expensive (QIDO is $150). You can buy a nice keyboard (with the option built in) for less than that price.
