I think you should just put the sticker on top of your ds and spray paint. I would end up looking somthing like this
Here's what you do
-Clean you DS. Go over the front of you DS with a dry cleaning cloth like the ones used for cleaning glasses. Don't use paper towels as they can leave tiny scratches on the DS. Do not use water or any cleaning solution. You just need to buff away any smudges so the paint will adhere.
-Put the sticker on your ds. Don't actually apply the sticker though. This will make it too difficult to remove later without scratching the spraypaint. Just place a bit of double-sided tape on the back to keep it in place.
-Tape off you DS. Cover all parts you don't want to get paint on like the hinge sides and back. Simple masking tape will work best for this.
-Paint. Use a paint that will adhere to plastics without any sanding or other preperation. I recommend using Krylon Spaypaint for Plastics. I holds very well and dries fast. Be sure to practice painting on something other than your ds first, like a cardboard box. Once you get the look you want on the box, move to painting your DS. Be sure to paint in a well ventilated area like outside. Also make sure to paint on a surface that can be discarded later. You can just use the box you used earlier to practice on.
-Wait. The paint may take a bit of time to dry depending on things like the type of paint, humidity, temperature and things like that. Take a look at the paint and see how long it is supposed to take it to dry, and then wait for that period of time and perhaps even longer to be sure.
-Remove tape and sticker. Only touch painted parts of you DS when you are 100 percent sure they are dry. You don't want a fingerprint on your DS. Carefully remove all tape with a fingernail. Do the same for the sticker. If you only secured it with some tape as I recommended, it should come off easily.
-Enjoy! You now have an awesome DS unlike any other.
Hope this helps! I'd like to see what it looks like when you're done.