Can these units be hard-wired?

Yes: 1) Clip off the cigarette lighter end and connect the red wire to 12 volts and the other (white) wire to ground. Add an in-line wire fuse to the power side (red wire). The fuses should be a 5 amp/fast burning type. 2) The power cord with the solid white stripe. Connect the white stripe (ribbed) wire to 12 volts and the other (black) wire to ground. Add an in-line wire fuse to the power side (black-white wire). The fuses should be a 2 amp/fast burning type. 3) The power cord with the dotted white stripe. Connect the black wire to 12 volts, and the dotted white stripe wire to ground. Add an in-line wire fuse to the power side (black wire). The fuses should be a 2 amp/fast acting type.