Although I never went as far as to fully stat them out, I gave some thought to their classes, based on what I know of their stories.
The Mouser started out as a wizard's apprentice, then moved to Lankhmar and became the quintessential rogue, so he'd have to start as a Wizard (or maybe sorcerer), then rogue, then possibly duelist. I'd say Wiz3/Rog10. Of course, he must have Two-Weapon Fighting and Weapon Finesse to take full advantage of Scalpel and Cat's Claw.
Fafhrd had a dabbling in sorcery while in Cold Corner, but no more than that. He'd be a Bbn8/Rog4/Sor1, just to keep him at even levels with the Mouser. Power Attack seems about right for him, and he probably has Weapon Focus (greatsword) and Improved Critical to wield Graywand to maximum effect.