Carbohydrates in rum are going to come from two possible sources: extracts from the barrel and additives.
Most aged rum will pick up some sugars from the barrel at a relatively low level, as rum barrels are typically not new oak. These levels will vary by producer. Some producers may then add extra sugar or caramel coloring (sugar) for sweetness, body, and color. Aged rum from reputable producers shouldn't have much sugar [anecdotally, Zaya and Pyrat seem to be exceptions], but you have no way of knowing from the label.
Most spiced rums will have sugars (and potentially other additives, like glycerin) intentionally added for extra sweetness, which helps the producers make a mass-marketable, smooth product without too much time in the barrel. I'm not sure I'd trust any spiced rum to be sugar-free.
White rums should typically be sugar-free, especially those with the word "dry" on the bottle like Flor de Cana. These don't spend much time in the barrel, tend to lack additives, and are filtered. You should be safe to start with a good white rum and add your own spices.