Did the 10 luck reduce you chances of critical failure? And did being a melee or unarmed character result in less grievious injuries to yourself for rolling a critical failure?
I think that luck decided the chance of it. Not 100% sure though.
And about melee and unarmed, you will still get critical failures.
The difference is that the melee weapon can be picked up and reused.
And Unarmed weapons don't break IIRC.
While small/big/energy breaks and can't be repaired.
So it's a lot more economical to play a melee or unarmed character with jinxed.
Or you can just be a diplomat and try to stay out of fights and use sneak a lot.