What if Swain used his cane to walk while slowed?
Some champions have a unique walk animation while slowed. Off the top of my head, I know Tristana drags her cannon along the ground.
Seems like this would be a neat spot to have Swain use his cane. Also averts the problem of his limping on a cane looking silly at high movement speeds.
(I don't know if he already has a slowed walk animation or not, I haven't seen any in-game footage of him.)