you could re-instantiate it.
Here are the options:-
var options = {
now: "12:35", //hh:mm 24 hour format only, defaults to current time
twentyFour: false, //Display 24 hour format, defaults to false
upArrow: 'wickedpicker__controls__control-up', //The up arrow class selector to use, for custom CSS
downArrow: 'wickedpicker__controls__control-down', //The down arrow class selector to use, for custom CSS
close: 'wickedpicker__close', //The close class selector to use, for custom CSS
hoverState: 'hover-state', //The hover state class to use, for custom CSS
title: 'Timepicker', //The Wickedpicker's title,
showSeconds: false, //Whether or not to show seconds,
secondsInterval: 1, //Change interval for seconds, defaults to 1,
minutesInterval: 1, //Change interval for minutes, defaults to 1
beforeShow: null, //A function to be called before the Wickedpicker is shown
show: null, //A function to be called when the Wickedpicker is shown
clearable: false, //Make the picker's input clearable (has clickable "x")
};
$('.timepicker').wickedpicker(options);
so in your button click
, call:-
$('button').click(function(){
$('.timepicker').wickedpicker({ now: "12:35" });
});