I think you will find that peels with round blades are generally harder to find and are usually quite a bit more expensive than those with rectangular blades. Also, once you start getting to the larger sizes, like 16" and above, the prices start to increase and you may not hit your $20 benchmark.
If you are willing to accept a wood peel with a rectangular blade, you may want to check out this website for Instawares: http://www.instawares.com/wood+peel.0.3.1-0-0.htm?sessionID=13218A92241812DBAA830130
. If you can find a peel that interests you, you can use the checkout feature and use the calculator provided to estimate shipping charges. Instawares also accepts money orders (look under Payment Methods in the right navigation column). If there are any doubts after going through the exercise, there is an 800 number for you to call. You may also want to check to see if there would be a sales tax due on any purchase you may make. You might also discover that the amount of shipping charges may allow you some slack to buy other items without increasing the total shipping charge.
You will note a wooden peel that is 14" x 16" x 24" for only $9. A 24" handle may be too long for your purposes but it would be easy enough to cut it back. Or you can get the peel (e.g., 14" x 15") with the 9" handle. Or any other that suits your fancy.
Another possibility is to see if there is a restaurant supply store near you that sells pizza supplies. If you can find the size peel you want, you will save shipping charges although there may be a sales tax involved depending on where you live.