I bought some nytes I wanted to make into old designs updated from before the revamp, but then I found the regenable traits were different for each one, and I couldn't make the design I wanted to.

How can I check which traits can be regenned before I buy a pet?

As far as I know, you can't. You could ask the owner before purchase, though!

with nytes the regenerable traits are entirely based on what they had before the revamp (the only times they get free pick is when the traits they had aligned in such a way that they'd completely lose trait points, at which point they get free pick for the trait slot where they used to have a trait but no longer do, or if they had a mutator used on them prior to the revamp, at which point they get free pick of all traits (for greater mutators, I assume the same of lessers, and probably pets that had lovely/lucky mutators, at least if they were used for non-res traits?)

So yeah, best off pm-ing the owner to check traits