You couldn't really 'walk' it around the peaks nearby. The closest you could get is to walk up the valley west of Gokyo, cross the Nangpa La, coming out near ChoOyu BC then walk across to Ev BC from there. Long, but quite possible. Tibetan refugees regularly do part of that.
Or if you could do some glacier travel, with maybe a little climbing, you go up the Gokyo, up the Nup La, down the West Rongbuk, back along the Central Rongbuk and to Ev BC. Shorter than the former option, but more technical. Hillary and Lowe did this illegal trip in '51 or '52, then Sayre and friends in '62. Don't know of anyone doing it since.
Expeds have climbed Khumbutse (west of the Lho La) to gain the Lho La, rather than climbing up to the Lho La from Ev BC Nepal side (v hard), so you could descend to north side Ev BC that way, but that is much harder and more technical. A Belgian climber did this illegally in the mid 80s - Nepal BC-LhoLa-Rongbuk Gl-Ev BC.