It depends on what bindings you are using. Chomps will work with old Spark bindings. The Burner and Blaze. If you are getting a Tesla (you should it's freaking sweet) set up, you'll need the Sabertooth crampons. Karakorum has their own and same thing with Voile.
As for using ski crampons. I used mine all of twice last season. Once in Washington skinning up the swath couloir. It got firm and fairly steep. Even then I was right at the limit. The other time was last spring when I did the Northwest Couloir on Torreys. I didn't necessarily need them, but it was a whole lot less work to use 'em. As the beat up skiers and spitters without them can attest. If you are doing the 'dacks, which I assume you probably will, I would think you would want them. You'll also want boot crampons and probably an ice axe. From what I've seen of that terrain, it is frequently required to get to where you are going. The Adirondacks have serious mountaineering type of terrain. May not look as glorious as say what Washington has, but it is still the real deal.