It would take quite a while for everyone to figure out the cosplaying wizzie is an actual Wizard. Heck there are some self proclaimed Grand Warlocks and such here in our own RL world and we don't automatically assume "gosh, magic!"

The Wizard would have ample amounts of time to acclimate to the situation at hand. And remember its only one Wizard 20. If an entire nation or empire of Wizards decided to come to our world, then that's a different thread entirely.