I would use a relay. Tap the Accessory of the radio for the coil(turns on relay). Then tap the power from the Lighter socket. This is where power would draw. This won't overload the accy pos on the ignition switch.
Relay Pin out
I would apply Accy power to pin 86.
Take the tap from the cigar lighter to 30.
Attach pin 87 to the XM radio 12V power.
and Tape off 87a(This is on when pin 86 does NOT have power.
Or use a 4 Pin 12v Relay. Layout is the same, Except the middle pin is missing. This is Normally Conducting power when the Relay is at rest(car off).