This is a tough one. I tried subbing rum into a perfect Manhattan and didn't care for it. I make a tiki old fashioned that's been a big hit and it's not too sweet, but it's definitely not dry. That's still the best "dry" rum cocktail in my repertoire, so I stuck with the old fashioned format and worked on a different variation. Here's a rum/coffee old fashioned.

1.5 oz Plantation 5-year, 0.5 oz Wray and Nephew 151 0.75 oz Perc, 2 dashes Angostura bitters. Serve on ice with a wide orange peel.

Smells of coffee, alcohol, and orange. Tastes of a strong earthy coffee sweetened with molasses. A little bit of banana, and a little bit of warming spice. Not too bitter and not too sweet.

Notes and other thoughts: There's probably a better rum or rum blend. Also, the 1/2 ounce Wray and Nephew is an estimate. I tried it with just Plantation and thought it needed more punch, so I put in a splash of the 151 and it helped. It's probably less than that amount. Perc is a regional coffee liquor, I don't know if it's available outside of New England. Kahlua would not make an acceptable substitute, but I think Mr. Black would. The orange peel isn't a great garnish for this. It doesn't mesh well with the other flavors. Not sure what would be.

I got two suggestions from another site, including them here, not as entries but for anyone looking for a suggestion. The consensus on that cooking community was Barbancourt Haitian rum, on its own, is not sweet and is good enough to just sip. Their suggestions were:

Barbancourt rum with ginger juice and bitters.

Barbancourt martini with dry vermouth.