I tend to prefer grappling hooks when they are taut and predictable, but 2014's Spiderling [official site] wrings satisfying physics puzzles from the springy, sticky web its main character can fire. It's a free game that runs in your browser and it'll eat up your afternoon.
I discovered this game via Free Game Planet, which is also where I pilfered the below GIF from because I couldn't capture from it myself. Go read their website. It's a good source of free games and they're cleverer than I am.
The pace and atmosphere of the game remind of Knytt. There are sparkling lights hovering in the air, harmless frogs hopping around your feet, enormous snails which recoil inside their shell when you approach. It's languid and quiet.
By comparison, the challenges you'll have to face are quite tricky. You fall slightly faster than your web fires, which makes it tricky to time consecutive swings when dangling from ceilings. The spring web makes it slightly tricky to time the grab and release of objects, as in the above GIF, a puzzle which took me about 12 attempts to get right. But it's fun and it's not too long and your discarded webs drape pleasingly over the scenery by the time you're done with any given room.
If you get stuck, you can find a video walkthrough of the game by creator Martin Petrini below: