'Rien n'arrive sans raison' for tattoo, would this be correct?

I've been thinking about getting a tattoo on my ribs like curved under my boob if you know where I mean and I've finally found a phrase I like the look of. More so because with my decent knowledge of French I understand it without much thought and of course the length would be perfect too.

Initially I was thinking of a literal translation of 'everything happens for a reason' but after some looking about I really like the phrase 'rien n'arrive sans raison' so that would be 'nothing happens without reason' (correct me if I'm wrong please) and still basically means the same thing.

I just need to know if that would come across as an awkward translation to a French native speaker? Also it does basically mean the same thing in France and I'm not getting something too far away from 'everything happens for a reason'?

Thank you for any help!