The sole compensation of the coroner and deputy coroners for attendance at an inquest and for any preliminary investigation under this chapter at the direction of the district attorney shall be a reasonable sum set by the county board for each day actually and necessarily required for the purpose, and a sum set by the county board for each mile actually and necessarily traveled in performing the duty. Any coroner or deputy coroner may be paid an annual salary and allowance for traveling expenses to be established by the county board under s. 59.22 which shall be in lieu of all fees, per diem and compensation for services rendered.