The Fellowship characters will still be around doing the various periphery things that don't directly relate to getting the ring to Mount Doom, but Doom Guy starts in the Shire with the ring, an indestructible map, and the basic knowledge of what it is and what needs to happen. He also has a chainsaw with unlimited fuel and a flashlight. For the purposes of this thread, he will just see the various evil creatures out of Mordor to be the same as demons. Various characters who helped Frodo know that he's coming, so he will still be able to get things like boats if absolutely necessary. Two scenarios:
1. The Ring is functioning entirely as normal. Can the mechanics of its manipulation impede Doom Guy? I pose this one because he has a history of being laser focused on objectives and being nigh on immune to subtlety (obviously he still has to get where he's going regardless). In this scenario, the map also gets fuzzy around Moria and will force him to take about as much time to navigate it as the Fellowship did.
2. The Ring functions as normal except that it has no direct effect on the Doom Guy regardless of whether it would or would not. Map is perfect.