yeah, you can do it if you have a brake. but if you aren't running a brake, you ABSOLUTELY need a new rear wheel. A lot of times track bikes don't have lockrings, but they also don't skid. Go to benscycle or Bicyclewheelwarehouse, and you can get a COMPLETE wheelset for like 90 bucks. It's worth it. Not being able to skid is no fun! Besides, peace of mind goes a long way b/c you will have more confidence to ride hard and that is more fun, too.

Also, post a pic of your bike plz. I have a conversion that I believe to be an 87 strada, but I can't be sure.