The better way to do this, if you want the power switched, is to create it's own circuit directly from the battery, then use an inline fuse and a relay to energize it. The radio circuit can only handle so much load. It should easily handle the extra load of a relay, because a relay is designed not to use that much current in and of itself. By attaching the relay to the radio circuit, it would be providing power to your charger at the times you are looking for it to, but the draw on it would be quite minimal. In turn the relay would provide the necessary power for the charger and the FM bypass.
When connecting the relay, ensure the one you chose will have enough Amperage rating to cover the need. I'd suggest a 40A relay with a 40A inline fuse to match would do the job. Then you'll also need to get wire of the correct gauge to cover both the powered side (coming from the battery) and going to ground. Looking at this chart, I'd suggest a 10 gauge (12 would probably be more than adequate) wire will have you covered. It will probably be a little bit of overkill, but with wiring, too much is better than too little.