Nesh also means a fancy dan footballer (like those of Sheffield Wednesday) who flinches away from a tackle with a no-necked full back who had been fed on raw meat.
Example in use: "Tha's neshed it".
Derivation? Well "nose" probably and frightened of getting broken. Similarly Dave Higham's explanation of being frightened to go into the sea at Brid at Easter applies also. Frightened of some part of the anatomy - here nose is a euphemism - dropping off.
Though I must admit a modicum of surpise at M. Higham as we call him now forgetting the origin of Medup. I blame the wine.