It should certainly be in the singular and it would work perfectly well with the definite or indefinite article.
I would like a hot dog without a bun.
I would like a hot dog without the bun.
One hot dog please. No bun.
Technically, however, it's only a hot dog if it's a steamed sausage in a bun. Without the bun, you just want a sausage (or a frankfurter, in BrE).