I need to fly from Italy to Switzerland in my aircraft with N markings. I've been told I need a clearance from a customs office within an airport prior to crossing the border. Is this true?
It's true. You need to take off from a authorised Airport with customs in Italy and land at an airport with customs in Switzerland as your first stop.
Here is all information you need including a list of airports with customs. https://www.ezv.admin.ch/ezv/en/home/information-private/waren-anmelden/einfuhr-in-die-schweiz/warenanmeldung/grenzueberschreitende-fluege.html
It's not to do with the N-markings... ANY aircraft that wants to fly between Italy and Switzerland needs to fly between 'Customs airfields'. Note - you don't need permission from Customs, just to leave and enter via a Customs airfield, reporting to Customs at those airfields.