From your post I assume you have the stand alone unit with the RF receiver, and NOT the new head unit with siruis built in.
Find out which wire is positive and which is negative (on your sirius power cable) in the following way:
when you cut your cig lighter plug off, mark which wire used to go to which wire.. (so you can identify it later..)
after you have cut your cig adapter plug off...
use the adapter and plug it in to your cig lighter, with only two wires sticking out.. make sure they are not touching each other or anything else.
use a multimeter and measure the voltage from one wire to ground (any unpainted metal surface that is connected to the body of the car... a screw wouldn't work if it is going in to plastic or the dash... but a screw on the DOOR would, or the door itself..
if the voltage is 0V.. then that wire is negative.. measure the other, it should be 12V.. that is positive.
remember when I said to mark the wires as you cut them? this is why.. we now know which wire is supposed to be hooked to the positive to lead to your radio.
To splice the wire you would have to remove the radio, at least enough to see the wiring harness, and GET to it.
Use an inline splice

to splice in to the ignition power..should be marked as IGN, or "switched PWR", with the positive half of wire leading to your sirius.
Lead the negative wire of your sirius power cable to ground.. and you now have switched power.
This would all be done AFTER MOUNTING the receiver unit where you want it, and AFTER ROUTING the power cable through whatever means you want to hide it, and to the rear of the radio. (makes no sense to splice it while its in the open THEN try to route it or hide it..
If this is confusing let me know, and I will draw something up..
Ray