Here is the final idea for wearing these skinny scarves.
This is the original vintage scarf  I bought a good while back. One benefit of a skinny scarf is that it if you wear it long as in the picture, it creates a vertical line which lengthens the upper torso.
And yes it is scooter friendly as it keeps my neck warm where the wind creeps in under the helmet. I find wearing layers easier as I can take them off when I arrive wherever and put them back on when it’s time to get back on the bike.
Scooters are also skirt friendly unlike a regular motor bike. Well mine is. Just not a super narrow pencil skirt. Although having said that I have had my skirt blow right up.