Very formal, tending to archaic: 'perambulate'. Originally the word 'pram' was an abbreviation of 'perambulator'; but as with 'bus' - from an original 'omnibus' (Latin omnibus, 'for all') - an apostrophe would be excessive. (This and its derivatives can still be heard in real life - at least in some circles. A few weeks ago, at Lord's Cricket Ground, when the public were allowed to walk on the hallowed turf during the lunch break, the announcement was 'Perambulation is permitted'! ;-))
Much less formal, in fact downright informal: 'to go by Shanks's pony'.
b
PS I imagine a Google search would explain who Shanks was. It might not be related to a person, and the capital letter may have just appeared out of nowhere; one of the Johns (II, I think) had the nickname 'Longshanks' - shank was once a common synonym for 'leg'.