I had a quick look in the full OED, and couldn't find any mention of 'walck', 'welck' etc, just the word 'walk'
"In a church or other public building: a place where people can walk; an ambulatory, cloister, aisle, portico, or the like; esp. (in the Royal Exchange in London) each of the portions of the ambulatory formerly allotted to different classes of merchants and designated by special names, as East India, Virginia, Jamaica, Spanish walk, etc. (see diagram following the passage in quot. 1766)
e.g. 1766 J. ENTICK Surv. London in New Hist. London IV. 102 In this area merchants..meet every day..and, for the more regular and readier dispatch of business, they dispose of themselves in separate walks, according to the following plan."