I'd be less worried about riding on the track than riding on the road. The riding surface is better, there's no traffic to deal with, better not be any dogs to avoid, no gravel or debris, no one else has brakes so they won't be slowing down suddenly either... I took a free course at the Lehigh Valley Velodrome about 15 years ago, and it was a lot of fun. They have been fortunate that the Air Products company (blatant sponsor plug) has been sponsoring a program there for at least the last 20 years or so. Hopefully the velodrome closest to you has a similar program.
__________________
The rider in my avatar is David Etxebarria, not me.