Good junglers for a passive playstyle?

So when I jungle, I tend to avoid duels with the enemy jungler and only go for super safe invades/ganks, where I'm confident, I get something out of them and survive. This essentially leads to pretty low Kill Participation, but also few deaths for me. I figured I'd pick up Kayn for this playstyle, because I thought his weak early game would syngergize with my playstyle. However, I keep having the problem of taking so few fights, that I only get my transformation at least 15 minutes into the game. Then it feels like the game's already decided before I can start having an impact, even though I track the enemy jungler and get my teammates to avoid ganks. So am I playing Kayn wrong? And what are other junglers (except for Yi, I suppose), that complement this playstyle?
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