The Shorter Oxford English Dictionary gives shore¹ (sea-shore etc) as coming from Middle Low German and/or Middle Dutch schöre, perhaps from the same base as 'shear'.

Shore² (a prop or stay) also comes from Middle Low German and/or Middle Dutch schöre - a prop. But it's not clear whether these are the same or two different words.

And shore³ is a sewer:

Shore, sb.³ 1598. [orig in common shore, perh. an application of this phr. (SHORE sb.¹) in the sense 'no-man's-land at the water-side, where filth was deposited for the tide to wash away'. Not a var. of SEWER sb.¹ (common sewer is later).] = SEWER sb.¹
Olde receptacles, or common-shores of filthe. SHAKS

Wassail! V