Dummy Ultrasonic Transducer
what passive components could be used in place of the removed
  transducer?


The dominant equivalent component is a capacitor. The value varies from transducer to transducer. A measurement of one example was 1.3 nanofarads.
Since the circuit is unknown, it is impossible to say if a transducer should be replaced with an electrical equivalent...no replacement part would likely cause no damage. Try it.


  Can I just wire the transducer with short extension wires? Should the
  extension be shielded?


Yes, some inches extension should be OK. Shielded wires would be OK, but simply twisting those two insulated wires together should do just as well. Electrically, pulse timing is affected an extremely small amount by an extension, but acoustical pulses do change to a far, far greater degree. You can safely ignore the electrical effect of an extension provided it is not too far.