The classic solo confrontation for Wolverine would be the Hulk. There's a few fan-made write-ups for the Hulk around in the event that they still haven't posted the much-awaited official stats for Hulk and Thor by the time you want to play. I like this one personally.
Have the Hulk rampaging around in the Canadian wilderness just north of the US border and heading toward an inhabited area. Wolverine is sent to stop him, or at least lure him into rampaging in a different direction.
This would be an especially good showcase for the MHR system because Wolverine has little chance of defeating the Hulk by leaping in and trying to inflict damage. He'll need to make creative use of stunts, assets and complications to win.
Another good Wolverine one-shot is found in this truly excellent list of action scenes here.
"Ninjas on a Plane" could be run as is, though for Wolverine the setting might be best changed. But the enemies are a horde of Hand Ninjas led by Lady Deathstrike, thus being a very suitable opponent for Logan.