As long as you aren't trying to run a hair dryer off of it, this adapter should do the trick. It isn't grounded, which means it I would not expect it to do very intensive work, and some plugs may require you to fill the grounding peg hole to get a current. You should have some sense of supervision if you plan on drawing any more power from it. Though this adapter does have its problems, but it is quite lightweight and will get the job done for your purposes (and your 3ds).
Yet another answer is to use a 5V USB charger to charge your 3ds, and that will do a fairly good job without the need for a converter.
You can also just get a 220V 3ds charger/adapter, as they are very cheap.