Mach 3 to DE adapter?

I was wondering if there’s some kind of adapter out there that allows you to use a cartridge with a DE handle? Seems all you would need is a screw thread on the bit the cart goes on. I’ve got a few Mach 3 carts but the handle feels really light after using my EJ DE89 and twig.
This probably looks like what you're after but don't know if the handle unscrews from the metal mach 3 bit.
Whether it's worth trying to do much about it will depend on how many carts you have left to use up, seeing as you already have a good DE setup. I keep my old Mach 3 carts for if I need to travel by plane and can't take blades.
All those I've seen were using either M4 or M6 threads, and there are handles with such threads to go with them.
I think there were some M5 to M6 adapters floating around, too, but no nice looking ones.

Maybe this could work, but I haven't tried it:
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