If you list it on here for a relatively decent price you'll sell it quickly. If you need the money, I understand. If you really don't, I would hold onto it. The Heavy Duty is one of the all time classic S&W revolvers. I have a 5" one from 1952. It's one of my favorite revolvers, and I even carry it occasionally. It's in about the same condition as yours, with the correct stocks. It would be one of the last to go if I were ever going to start selling stuff. If you sell it, I'll bet you'll regret it, but it's your choice and your revolver, so do what's best for you.
You mention you don't handload. Neither do I, but that hasn't stopped me from enjoying shooting it. Take it out and shoot it again. Bet you'll keep it.
Jim