Pretty much every mage with spell vamp can heal during Zhonya's. A lot of them have ways to deal damage while in stasis to, Annie's Tibber's doesn't mess around.
Concerning Zhonya's interaction with Swain (and Fiddlesticks and Morganna and Kennen and Karthus), look at it this way. The main reason to pick a mage is because AoE.
AoE has very minimal use in a 1v1 scinario, which makes the big draw of a lot of mages team-fight potential.
Which essentially means you're optimal play style with a champion like Swain involves hurling yourself into the middle of 5 hostile champions. Really close to them as well - seeing as it's an AoE centered around Swain himself, not a projectile he can lob at his foes (like Ziggs, Orianna, Gragas).
that...is a pretty stupid strategy when you really think about it. Without Zhonya's it also would be pretty much impossible to do.
Riot is well aware of that interaction to, Zhonya's stasis has been around from when LoL originally went live (Originally as Zhonya's Ring). Hourglass is also in the recommended builds of all the champions I mentioned, so there's also that.
Also - Swain can't move while he's golden, so just back off, lay a trap at his feet, and take the opportunity to gain a positioning advantage.