You can do that, if you're a stealth character who's fast, good at sneaking and (optionally) has spells like chameleon or invisibility. But a Nord isn't exactly know for his lightfootedness and magical ability.
No worries though, you can just as well become an assassin in the less subtle sense of the word: someone who just rushes head on and smashes skulls. It will cost you some cash and a lot of trouble on some 'endeavours', but nothing bad on the whole.
Good luck with your char, looking forward to your progress!!
