Exhaust is a good idea, and so is fiddlesticks (if you're crazy enough to fiddle mid). Malz seems to work well (I don't have him), Kassadin has silence (I probably don't have him), and Xerath might work well but doesn't have skillshots and presumably doesn't bring any sort of healing along with him.
I think that laning as Leona against Katarina would be a terrible idea against Katarina because of the lack of damage. You don't need the ult to kill, you just need to be able to harass her out of lane with Q, unless she somehow has enough HP regen to survive that.
Contrary to what you might expect, I really don't think Galio is a good choice. I went against one last night, and despite his magic resist stacking (both big item and little item), I was like 30-40 CS ahead of him and kept knocking him out of lane. I lost the game though, partly because I left his tower up because I didn't want to lose the farm I was getting, and partly because that might have been one of the Teemo Games (i.e. Teemo + whoever were 1/15 combined bottom lane and I hadn't ganked so it was partly my fault). And presumably partly because I was a terrible player and died to the jungler 2-400 times.
The big deal with Galio is that he's skillshot, and a good kat should dodge most skillshots, meaning his Q harass will just take his mana and probably won't hurt Katarina. If you're farming well and hitting him with Q and building sorc shoes and have magic penetration masteries/runes, you'll go through some of his magic resist already. The only healing he's probably going to have early is the shield, and is that something that heals a lot and can be spammed? Didn't seem so as far as I can tell.
And how about that ult? Well, unless he's being ganked, here's how that works. Harass with Q, get Galio low, ult if you feel like it...oh wait, he ulted? Well, now he's low health, you survived his ult presumably without taking much damage, and now you have like 45 seconds until you can just ult him again, while he has maybe 100-120 seconds to wait.