Ugh, if it's Sutter..... gross.
Horvat (or even Boeser) would be the obvious choices if not for the fact that it might hurt their development to heap all of that on them so early. That said, he's admirably handled everything else that's been thrown at him like a veteran so far, and doesn't strike me as someone who could be phased by that, so maybe it would be fine to just give it to him.
Three As is probably the best option right now. Nobody is perfect for the role.
It's not ideal, but I wouldn't mind giving it to Tanev as a stop-gap until Horvat is ready though, to be honest. Despite being a soft-spoken guy, he's not as passive and anti-wanting-to-take-on-a-leadership-role as Edler is, he's the best and most important player on the team by a country mile, has the best work ethic, consistency, and influence on other players, and in my opinion, it's not a good idea to trade him. On meritocracy, performance, and on-ice-leadership, he's the clear choice, and on personality, his lack of suitability is blown out of proportion, IMO.
My off-the-wall dark-horse pick would be Sven Baertschi. Will likely be around for a while playing a pivotal role on the team with our best players, isn't too young to heap that responsibility on him, has been a key piece on the team for long enough that it wouldn't feel like a complete joke, pretty well rounded and hard working player, more suitable demeanor than Tanev or Edler, and seems like the kind of guy who thrives with added responsibility or a spark lit under him. While he wasn't the captain, he handled carrying the team on his back and having massive amounts of pressure heaped onto him admirably that one year in Utica. It honestly wouldn't surprise me if slapping a C on him works the best out of everyone on the team. Unlikely to even be considered, though.