Having and using a radio may not keep you safe, but it will keep you safer. Like flashing beacons, strobes and paint schemes, radios help to make your presence more "visible" to others and, for the life of me, I can't understand pilots flying without one.
If you spend $30, $50, $100k on an aircraft and probably $20k or more learning to fly it, the cost of a radio is a small investment in personal protection (ditto a PLB and decent safety harness).
Ian will sell you one for less than $400
Icom IC-A15 AUS
$374.95