It would have to be doubles, because if you play singles with Skill Swap, you're essentially leaving everything up to chance. There's also nothing with a disadvantageous ability that can learn Skill Swap, e.g. Truant.
In doubles, it's mostly with Truant that people use skill swap, Slaking being the main one. You have Slaking and something that can use Skill Swap, e.g. Blissey. You Skill Swap Truant with Blissey as Slaking attacks, and then get Blissey to Skill Swap Truant to an opposing Pokemon to make them useless every other turn, and while they can just switch out, it's presumed that it's not a particularly desirable option, as switching in doubles is much more risky than switching in singles.
I have to say though, Skill Swap is pretty gimmicky. For all its worth, you could spend the time using Skill Swap doing something more useful, like setting up screens, or using Pokemon with abilities like Drizzle + Swift Swim, which activate on their own and don't waste a turn.