That seems to defeat the point of replacing it. 
As I understand from HUSBZB-1 Z-Wave firmware portion update, updating the Zwave firmware involves cracking the stick open and shorting some pins.
I guess I’ll just go and re-do everything with the news Zooz controller, and as I do that, record the DSKs. I guess I should have saved all of the boxes with QR codes in a scrapbook or something, but I didn’t, so I’ll have to go to each on anyway. I’m finding the QR code reader in HA to be pretty flaky — it annoyingly wants to use the front camera every time, and I can’t use the one in zwave2mqtt in a phone browser because I don’t have that set up wtih SSL.
Plus when I tried SmartStart before, a few nodes never showed up, and another showed up without encryption even though they supports that. I’m hoping the updated firmware fixes that.
So all of this is to say… I guess what I’ll do is reset everything and re-include with the new stick. But, it does look like the DSKs can actually be read from the controller, which will at least save me needing to record those manually — . I do find it kind of strange that zwave2mqtt doesn’t just store that “naturally”.