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I'd say Runesong dagger and chain donations + other quests are your best bet. Anything else is a might slow. Not to mention that a Runesong is still good vs other heros and the like.
lol. If runesong dagger could damage heroes, don't you think it would be in every deck that could use it?
Well it'll double the speed for Boomkin... anyway there are weapons which does damage to a hero (through non combat methods). A few are mentioned above by Gdrad (minus Runesong and Swift Discipline [you can't use that]). Sulfuras can't be used with Swift Discipline (reason is obvious), though it may stall the game for Pinprik as it attempts to find big burns to minimise damage (if it has DoT on you, feel free to laugh at him). Masterwork Stonehammer is another weapon which can be used (expensive!). Another out of box solution is to find Inventor's Focal Sword and redirect it's DoTs against him if he dares to use it against you. Alternatively, multiple Glaive of the Pit is another option.
Problem in all these solutions is that they are either redundant in the normal fights (Staff of Ogre Magi) or less effective compared to other cards available (Sulfuras and Masterwork Hammer).
Some people learn, some people don't. For me, I can never correct myself to say Julia Graves as opposed to Julia Roberts