It somewhat depends on whether you're talking USEF hunters or QH or other breed show hunter divisions.
In USEF classes, a pelham is absolutely fine for an over fences class. You absolutely won't look like an idiot. Some judges may look askance at a pelham in a flat class, with the logic if you need a pelham to control the horse in a flat class, they may not be an ideally quiet and calm hunter. That's some judges, not all. If I saw a pelham in a flat class, I might give the horse a little extra scrutiny, but if the horse was going in a relaxed, hunter-appropriate frame and had prompt transitions, I wouldn't penalize for it.
The best solution, IMO, is to show in the pelham over fences and the D-ring on the flat, if that's managable for you the day of the show. Lots of riders switch bits depending on the class, so you won't be alone in that regard either.