Green’s Dictionary of Slang

1. (Scot.) the penis.

2001		I. Welsh Glue 74: Ye ant tae huv seen this boot. Fuckin hell. N the size ay the welt oan the boy thit wis giein her the message.
2012		(con. 1980s) I. Welsh Skagboys 42: —Big laddie but, Mel, Les says suggestively. —Tiny wee fuckin welt oan it but, she scoffs.
2015		I. Welsh Decent Ride 40: When yuv goat a welt like mine it kin take ages tae git one ay they things [i.e. a condom] roond it.

2. constr. with the, the essence.

1969

(con. 1911) A. Baron King Dido 68: ‘I’d been shaggin’ the welt or your sister all that arternoon’.