I don't think this frame is that early, whether it's a skiptooth or not originally.... the serial number should be under the crank if it's a '51. It's on the left dropout. That's '52 up.
I was thinking a '61 frame with the A1 number, but it's supposed to be 6 numbers then and it's not, or doesn't appear to be.
If it was, I'd say it's a 24" girl's Flying Star, the smaller frame version of the blue one in the top right here:
http://www.trfindley.com/flschwinn_1961_1970/1961_04.html
But again the serial doesn't match that unless there's another digit out by the fender bolt hole... even then the Jan 61 numbers don't go high enough.
But a little closer look at the code list DOES turn up August 1953...
08/18/53 to 08/19/53 ------- A11749 ------------------ A19495
So that's a possibility. Darn those repeating sequences of serial numbers.
Which brings us back to what is it? The catalog pages, while such a great reference, don't show every model made. They'll typically show the 26" or more deluxe models and just mention off-handedly that they also offer a 24" model, a ladies model, a 2-spd or coaster brake model, or many other variations.
There don't seem to be any 24" models shown in 53 using that specific chainguard, but it's certainly in production if you look at some of the other offerings.
In '52, they built this exact bike:
http://www.trfindley.com/flschwinn_1951_1960/1952_07.html
I think it just wasn't shown in the '53 catalog. The catalog pics weren't always 100% accurate anyway- the text all says these bikes came with a rear carrier and clearly its not shown in the illustrations.
I would go with it being a Hornet but maybe some paint-color detective work will turn up something contrary to that.
It's nice but not worth a great deal of money, and I'd probably sandblast it, repaint it, get a set of repro decals, whitewall tires, and put it back on the road.
--Rob