I have a Khajiit that is in the 30s with zero kills.
Maxed up sneak and doing the same with lockpick, light armor and pickpocket.
All the level up points go in to stamina...running away from trolls and such is necessary.
No magic, no potions, no companions, no killing whatsoever.
It's fun...a unique challenge, but you'll miss out on a lot of quests that require killing.
I like the Khajiit because Night Eye is invaluable when sneaking through a dungeon where killing is not an option.