It’s not like I’m the first person with this idea, either. In the ’90s, Playmates released a line of TMNT figures dressed as classic Star Trek characters. They flubbed the line-up, of course—how is Donatello, not Scotty?—but the toys are still cool.
More obscure but no less cool was the appearance of DS9‘s USS Defiant in the original Teenage Mutant Ninja Turtles cartoon. It wasn’t an official crossover between the two franchises, but it was a fun Easter Egg nonetheless.
My proposal for this crossover would be either a comic book miniseries or an animated film for Paramount+—or even both. I mean, it worked for the Batman crossover. Either way, drawing the original series crew is really the only way they can appear in a Star Trek, Teenage Mutant Ninja Turtles project and still appear in their prime.