1962 Schwinn: what model
The real star here is the Bendix Red-Band hub.  They re-popped those racks and most of the original type parts for this for something like 30 years.  I've seen new racks like that as of about 10 years ago they kept making.  The part that really shows the age of this though, is that hub.  If that's an automatic 2 speed kickback, that dates it between 1960-1964.  So that would put it right in your estimate.  I take it there isn't anything on the other side of that chainguard?  I'd say it could very well be a Hornet.  Those tanks are removable, and someone could have done just that.