That was my intuitive feeling, but I must (now) admit "annular sector", whilst sounding nicer, is a contradiction: Like saying "circular sector". A sector cannot be itself circular or annular I suppose.
Yeah, it didn't sound this weird to me at first (due to this not being my native language), but it is. It's not exactly a contradiction I'd say, more like a definition turned upside down.
But yeah, "annulus" frankly sounds horrible.

Even if it's probably less correct, and more informal, wouldn't "ring sector" be appropriate, and sound better?