Can I purchase a nano SIM at the Kiosk and ask the employees there to transfer my phone number, plan, etc.?
They'll have to call it in to channel support but yes. Or you could just log into Self Serve and do it yourself online when you get home. Select the Mobile Phone tab and then go to swap phone in the bottom left corner. Follow the instructions there and once it's completed, just take the new SIM and place it in your new phone.