I hope there are copies around. The late Fabio Passaro, who did, I believe, the majority of the CG work for Eaglemoss, used Lightwave, same as the original VFX team. If they tried to reassemble that group, get their hands on as many of the original scene files as still exist, having many of the models already in the same format would give them a leg up. I assume he turned in the final versions of the models that he updated along with the renders.
The way I see it, creatively, they have a few options, from least to most invasive. For the sake of argument, we'll assume they have a comprehensive record of every CG shot from the show as-is.
1. Straight re-render. Use a vintage version of Lightwave, just load up the old scenes, change the camera setting from 720x480 to 1920x1080, hit "render," and Bob's your uncle.
Tom Smith did this with several original CGI shots from Babylon 5.
2. Mild updates for resolution. Keep the scenes the same, but replace the models with more detailed versions where the seams would start to show in HD. Most of the Eaglemoss models were detailed up for print, as were others used in the Ships of the Line calendars, so there are already offically-made drop-in options for several of the CG ships (and that would improve consistency, such as replacing the droopy-nose Defiant model and the Mirandas with impulse engines instead of torpedo bays). Perhaps replace lower-resolution effects, as well, like explosion elements. Put names on all the blank Galaxy and Excelsior class ships. Basically the TNG-R approach.
3. Bigger updates for modernization. Update the scenes and models for the newer versions of Lightwave which use a much more realistic lighting and surfacing system. Adjust lighting and effects for pop, and use a more modern post-production workflow. "What We Left Behind" seems to be a mix between "2" and "3." The models seem to be all the same, but the style was modernized (
the HD versions of the shots actually predate the modernization of Lightwave's render, they were made independently years before the documentary entered production).
4. Tweak the shots. More variety of ships in fleet scenes, replace reused footage with new shots. Dealer's choice if you want to restrict yourself to just designs that already existed but weren't available to the CG team at the time, or retcon in ships that weren't designed yet IRL but would've existed in-universe, like the Valdore, the California, the Parliament, maybe the Excelsior II, the Reliant-style Ambassador variant that wasn't in "The Pegasus," and so on. Likewise,
if you want to make Ron Moore happy, it's your choice as to whether marking the second Defiant as "NCC-74205-A" fits under this or 2.
5. Full TOS-R. Redo everything from scratch, worry about matching the spirit of the shot and not the letter. I don't think anyone really wants this.
I'd go for option four, myself. The show should look it's best, remastering the film will already cause a massive increase in production-value, the VFX should get some polish to keep up. Adding a postage-stamp-sized Constitution-refit or Ambassador zipping around in "Sacrifice of Angels," or the Romulans having more than one kind of ship at a time, will just make nerds happy and no one else will care.
Okuda talked about how they briefly considered having some of the ships in "The Ultimate Computer" be different designs, but decided that 40 years of inertia with them being known as Constitution-class ships wasn't something they could push aside. They didn't even make the Intrepid a new design, and we'd never actually seen that one in TOS, it was entirely assumption that it was a Connie.