The quickest way to activate the YP permit would be to fly out of Canada and back (but avoid the US).
Announced last week is the new option to request your YP permit by post. Though it's too early to know exact processing times, it's expected to take weeks to receive the new permit if applying by post, so if you go with this option, make sure you maintain status in Canada and stop working the day your WH permit expires if the new permit hasn't arrived in the mail yet. Instructions to apply by post are on the
IRCC website. Good luck!