wireless strain gauge
It depends if it's big enough to hold a transmitter, if it will be inserted in place and the patient will close mouth, thus shieding the transmitter.
If a portion of the device remains outside, it's quite easy, use a small transmitter in UHF ISM band with batteries or a SoC that has ADC, programmed for the job. Also zigbee
may be an option.
If it will be inside, i would recomment a passive device with magnetic coupling / near field communication in the style of RFID - at 125kHz or 13.56MHz, using a ferrite core antenna. I observed that magnetic coupling can easily be used from the other side of a few centimeters of tissue and bones, like the palm of a hand.