Book in for your booster jab as ASAP - I would explain to my GP practice the difficulty and ask to be booked as an emergency.
Only work deemed to be at high risk of sharps injuries requires Hep B sero-conversion ie assisting for oral surgery and re-processing instruments. Therefore the agency could send you for reception work and plain dental nursing (some practices have a decontamination technician doing the scrubbing and sterilising).
Some practices have a second nurse (clean nurse) when placing implants who basically just hovers to open packets, processes x-rays and wipes down the room in between patients ie not high risk of sharps injury.