Can anyone suggest a way to get to Woodside from anywhere in Wirral by road without passing a Pub (closed pubs and pubs gone included)

Yep - easy peasy - any route you like and call in at all pubs.

That has met your requirements as written

Snod (pedantic old git)

Ten out of ten Snod !!!!! Well done !

only one i can think off. From the roundabout at birkenhead/dock/tower road

tried that years ago - never reached Woodside after 5 pubs

if you mean Shore rd
Hope & Anchor Inn, 17, Shore road 1861 mawdsley
Ship, G. Lacey, Shore road, Birkenhead 1857 PO directory
Woodside Ferry Tap, 1, Shore road

if you mean Canning street
Canning hotel, Mrs. E. Berry, 1 Canmng st. Bfrkenhead
Egerton Arms Hotel Canning Street
London Hotel Canning Street to Lord Street
Pier Hotel Canning Street Hamilton Street

Nope, neither!
Mind you, my route can only be done 'on foot'