If you don't need window coverings for privacy, you might consider leaving them as is, uncovered. Let the view be your decor! Bamboo shades are nice, but it's hard to imagine cats not using them for play and scratching.

Unless your cats have a history of attacking window treatments, you will probably be fine with whatever window covering you like. Dangling strings ARE tempting, so the cordless options would reduce the risk of accidents. I've had cats (some of them quite psycho) for my entire life and none of them have damaged curtains or blinds or anything like that. I wish I could say the same for our current dog, who ate a pair of velvet curtain panels the first time we left him alone in the house. I didn't know a 25lb dog could rip down thick drapery fabric off its grommets and shred it all!

Roller shades would be the easiest, up out of the way except when you need them. Shutters are nice but it does seem they'd block the view. Maybe if you had them only on the bottom half?

What about Hunter Douglas shades that sit inside the window frames? No strings! They are able to collapse at the top or the bottom. Watch the video here.