It’s all about context; it just doesn’t strike me that this particular slang usage is a fit.
The “police” definition seems to have arisen among lowlifes in the early 20th century, perhaps earlier, apparently mocking the appearance of a uniformed policeman’s gait (what with them having sabers and all). Definitely not a compliment at the time. Nihon Kokugo Daijiten
2nd ed.  (someone dumped its entry here
if you don’t want to pay the ¥1575 monthly subscription for the online version) lists, along with a number of other definitions (plus some stabs at connotations, some etymology, regional variations...), gives attestations from 1915 and c. 1960.
I’m not finding much in the way of authentic examples, but in more modern times it seems to have become police jargon; e.g. it was shown in a 2003 TV show
, but it had to be explained to viewers and being in a TV show is no sign of authenticity anyway. It refers to a uniformed officer in that usage, too. A few explanations of this on the Internet even claim that it is not a well known definition (few hundred Google hits for “アヒル "制服巡査"”, though, and Ingo Daijiten
 lists it a number of times
; can’t be that
Other slangy references to a duck’s walk look to be quite obsolete (though Daijirin
seems content to list one of them as a secondary definition for some reason... I have reasons to doubt this remains popular usage). What it boils down to, though, is it has nothing to do with patrolling, but waddling or having a large bottom.