One of the developers said on ResetEra or NeoGaf that Cuphead was exclusive to Xbox and PC and that it wouldn't appear on any other platform. Studio MDHR published the first game, so this is almost certainly because of a deal with Microsoft (who partially funded the game and almost certainly used that money to secure exclusivity). If that's the case (and it's incredibly likely that it is), Microsoft would need to approve the game going to another platform, including the Switch. Sequels are a bit up in the air, because we're unsure of how the deal was structured, but the picture is pretty clear for the first game.
There is a chance the collaboration could be a Cuphead sequel, with both companies helping to fund the game/keep it off of PlayStation, but I'm not sure if that's a worthwhile endeavor for either company. Studio MDHR also owns the Cuphead IP and if Microsoft doesn't have some sort of right of first refusal, they can put it anywhere. They are also likely flush with cash because the Cuphead brand has been a merchandising juggernaut so far, so they would likely refuse any deal on a second game (especially one that included exclusivity) unless it was a godfather-type offer and just bring it to whatever platforms they wanted to.