1) Probably for ‘iron-shod’, used of a wooden implement furnished with a shoe or sheath of iron.
1485 j shod shole [shovel] ijd ob, Ripon
1576 two shodd forkes, two Iron forkes, Leeds
1632 one Iron forke one shodd Shovell and one shodd spaid 2s 0d, Scriven. A shod cart or wain was one with iron-bound wheels: 1515 unum le shodd wayne, ij oxen, North Frodingham
1557 ij unshod cowpes, Thornton Bridge
1577 for shodcartts ... 33s 6d, Beverley.