That is totally possible. If you go this route and if your dog continues with this behavior, I reccomend that you get a neutrik USB gender changer for the back of your case.
Get a 24mm Holesaw drill bit from Ace hardware and smaller bits for the screw holes to mount this.
Solder on and glue a short USB cable on the inside of your case and plug it into the inside. Once you know you have it on the PCB right you should hot glue that on.
That way if Fido mangles another cord you can just get another USB B cable, or disconnect it to put it somewhere safe.
Here is another forum where installing a Neutrik RJ-45 is part of the process. Similar port but the one I linked there is USB.