Silly question: did anyone ever confirm what insignia (if any) were worn by the Defiant's crew in "The Tholian Web"?
You mean on screen?
Going by the fact that Bjo Trimble's Star Trek Concordance
shows a completely different badge from that shown in ENT: In a Mirror, Darkly, Part II,
and one evidently of fan origin, by Robert Wood, I'd have to say that I really, really doubt it.