If you are outdoorsy people and really aren't that interested in museums, etc., then rethink your itinerary to focus on the activities that YOU enjoy. As another poster said, you can skip Florence, or indeed any of the cities. And I would very much agree, you are trying to pack too much in. (I LOVE art, history and culture, and on our first trip to Italy, we visited Florence and Venice, and then visited the more southern part of Italy on a subsequent trip; that way, we weren't traversing the entire country.)
Amalfi vs. Ligurian coast, I can't help much, except to share my own likes and dislikes. We went to Sorrento for two nights, because I really, really wanted to see Pompeii (and it is fabulous, especially if you are interested in ancient history). While the scenery was gorgeous, I didn't much like Sorrento otherwise, and I just don't love southern Italian cuisine (obviously, my very own prejudice). I like Ligurian cuisine a lot more (pasta with pesto, etc.), and do find the CinqueTerre enticing, despite all of the other tourists there. So I would vote for that area.
I did like Verona very much, a nice small city, though I was there when the opera was not on. Does your wife want to attend an opera? It does not look like they're performing on the dates you'll be in that part of Italy.
Even though Venice is obviously a city, it may be more interesting for outdoorsy types, as it's a city where you can do a lot of walking. I think the best thing to do in Venice is just wander around the street, admiring the canals and buildings. (Though there's plenty of excellent art, and a bunch of very interesting churches too.)
