I am sure that when you boat in on dry land you will be able to unscrew the locking nut and remove the existing transducer and it's through hull. If the wires are cut you can bet it will not work.
You can get the receiver checked out and if it works possibly buy a new transducer assembly.
However speed and depth systems are not expensive and it is likely much simpler to just repalce them. Most through hulls are a standard 2 inch hole so it should be an easy change out.