The FedEx link indicates the maximum box size accepted in a FedEx Drop Box is 20 inches long by 12 inches wide by 6 inches high. The box dimensions included with the question will fit in a FedEx Drop Box. Just buy and print a FedEx label online, apply it to the box you are shipping, and place the sealed parcel in a FedEx Drop Box.

http://www.fedex.com/us/dropbox/

yes there are no reactions using fed drop boxes