I'm in the process of converting a Martini to Hornet. Should be a neat little gun when it's done.
In my opinion, if you want to go Hornet then you might as well go with something antique or at least with an older flavor. It's a historic varmint round and is best matched with an historic action. If the end goal were strictly to have a 22 centerfire rifle, then a brand new .223 will do everything the Hornet will do and more, for less money. Nothing wrong there. If the goal is a gun with a different character than you get from a synthetic stocked Savage bolt action (again, I have no beef with that) then a low wall, Uberti baby rolling block, or some other interesting action in interesting wood makes a nice match with the old 22 Hornet round.
BTW, when the Hornet was developed way back when, the test rifles they used to try out the variations that became the new cartridge were '03 Springfields and Martinis. For what it's worth, there is that historical connection.
I think a Krag would be pretty neat too. For that matter, maybe even a trapdoor action would barrel up nicely. That may need a little bit of analasis to make sure it's safe, but the thought popped into my head as I was typing so there was no point in holding it to myself.