I'm not sure there'd be a Suigetsu in my version.
He always felt like an unneccesary member of Sasuke's team. Juugo and Karin both had skills that made them useful for tracking down Itachi which was the reason the team was put together while Suigetsu feels like some extra muscle they never really needed. He had his own ambitions that had nothing to do with Sasuke and really should have just gone back to Kiri yet went along him anyway and basically failed at everything he tried to achieve.
If I wanted him with Sasuke, I'd play around with his abilities and history some. His water body would be a kekkei genkai rather than a hiden ninjutsu and he wouldn't have been a shinobi of Kiri but an exile of the Land of Water. He's interested in collecting the seven swords but for his personal interests, not because he plans to be one of the Seven Ninja Swordsmen. So, like Karin and Juugo, he has no real attachments outside of the team.
But I'd prefer him not to be with Sasuke at all. Kabuto feels like a much better fit for me, far more useful to his goals and would provide an actual medic instead of randomly throwing in Karin's unexplained healing power later in the game.
Instead Suigetsu would be a loyal shinobi of the Hidden Mist and one of the Seven Ninja Swordsmen. If nothing else, it bumps up the number of relevant characters from that village when they start showing up from the Kage Summit onwards.