It can be done and it is safe.
Purchase one of these radio controlled mains sockets controlled by a hand held remote .... get it up and working your appliance .... note the appliance can be turned on by one button and off by another button.
Operate on a spare remote (it only uses a button cell) and solder a pair of wires on the "on" button terminals and another pair on the "off" button terminals.
From your 12 volt circuit connect two 12 volt relays in parallel with the second relay supplied via a correctly connected diode (which allows relay to function) and with a capacitor across the second relay terminals.
Now when 12 volts is applied the second relay comes on slightly later than the first relay. When 12 volts is taken away the second relay will switch off slightly later than the first relay (thanks to the capacitor fed via the diode.)
Now make the first relay operate the "off" wires on the remote and the second relay operate the "on" wires on the remote.
Surprisingly it should work as you required but will also switch off your appliance.
You will need to sort out the wiring of the relays but work logically ... all these bits and piece are available on the high street.
Double pole double throw relays will be required.
Not the remote is pulsed rather than the button "held" down at any stage so it will not drain the button cell.
The capacitor needs to be able to handle 12 volts electrolytic - slightly smaller than a chip (fish and chips) and needs to be connected with correct polarity.