"Waddy" is one of the words for cowboy, especially a cowboy who drifted from ranch to ranch and helped out in busy times. Jo Mora and Ramon Adams both suggest that the word derived from wad, something used to fill in, but this notion isn't widely accepted. Neither is the suggestion that it comes from chewing tobacco. To add to the mystery, waddy first meant "rustler", then "cowboy". Also spelled waddie.
Woad (also wad), is a plant grown, mostly in England to make a blue dye consisting primarily of indigotin. It was supplanted by indigo, then later by synthetic dyes. People who worked the woad plantations in the Fens of Holland, Lincolnshire, and Cambridgeshire still call it wad, just as it was pronounced 1000 years ago. People who worked in the woad fields were called waddies, or less frequently woadmen. (From Woad in the Fens by Norman T. Wills) It likely crossed the atlantic with migrant agricultural workers (cowboys).
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Desktop isn't much better.
No doubt, this page looks earnest and honest—but it also looks like a domain squat, or spam.
(Responding here to the mobile page)