There are very specific things I think need to happen for Skinner to get traded. It's only to Toronto, which he won't use his NMC on.
Thing 1 which needs to happen: the rumored Saros for Marner trade. Moving Saros makes sense for Nashville. He's 30 next season, his last under contract. Askarov is up and coming. And Nashville has a big cap hit coming for the 25-26 season when the big year of Duchene's buyout hits.
Nashville needs to improve it's roster while maintaining a reasonable cap. Adding Marner would be a huge add. Nashville's roster is flush with good soldiers but few big time scorers. Marner would change that. Plus, the change of scenery might help Marner become an even better player. Nashville is a small town compared to Toronto, and they'll love him there.
Nashville eats a lot of dead cap this season, and then they could allocate money which would've went to Saros to Marner. Then Trotz will need to fill in around Marner for a season.
For Toronto, they lose Marner but add the goalie that they need to get over the playoff hump. Toronto was way more dangerous when Matthews was in "Auston and the animals" role as the goal scoring center between two wingers willing to do the dirty work. So this is a step toward building a more playoff ready roster.
Trading Marner essentially voids their Bertuzzi-Domi-Marner line. Matthews would be the 1C with maybe Knies and another worker at wing. Tavares and Nylander are line 2. The defense is looking good and only needing 5-7 defenders. Kampf and Jarnkrok make up a good bottom six start. But they'd need more.
The Sabres step in an offer Skinner+ with 50% retention. The Leafs get Skinner for $4.5M for three seasons, which is reasonable. He could help drive a bottom 6 line in 5v5 play, which is what the Leafs need.
The Sabres free up $4.5M for 3 seasons, which they'll need.
This is the only scenario I see where Skinner is moved. A lot needs to happen and it's pretty specific. So, I don't think he's moved this season or bought out.