Did you know that back in 1950 or so, Lambrettas set some World (ie FIM) 125cc class records? I've also seen a photo of a Zundapp scooter setting a record on a banked circuit somewhere (Monza or Montlhery maybe) in about 1960. I'm afraid I can't remember more than that.
So you could be eligible for a classic, historic or vintage class if such a thing exists. Not knowing anything about the rulebook, I wonder if a scooter could run as a 125, 150, 175 or 250cc motorcycle, but it would be totally outclassed.
If you sit on the back seat of a standard 1960 Vespa 125 and lie so flat that you are looking under the handlebars, it is 7mph faster and will do 49mph