LEDs draw next to no current, but the fewer times you splice it the better.

Make sure that the total current draw on that feed does not exceed its fuse's rating, or it'll keep popping - you won't solve it by putting in a bigger fuse, as that'll just let more current through before it melts, which can be disastrous.

Depending on what you're actually adding to the wiring, you might be better off taking a feed from the battery (with a suitable fuse as close to the battery as possible), with some way of switching the power.

How come you've chosen to pillage the radio's wiring?