You have a nDS of some sort, but don't want to lower your router to WEP security just to use the WiFi function.
The Idea: Create a second WiFi network that utilizes WEP or no security.
The Solution: Use a USB wireless adapter stick that is capable of acting as a wireless access point.
Solution 1: Buy a used official Nintendo Wi-Fi stick. Nintendo hasn't produced these since around 2007, so you'll have to buy it used.
Gamestop has it for the cheapest at $14.99 in-store in a few remaining locations. When you get that, install the last software update Nintendo produced for it (from Nintendo support) on your computer. Note that this software does not support 64-bit operating systems. The stick will broadcast a WiFi network that only nDS (or at least the ones that you allow) can access.
Solution 2: Buy any wireless adapter that is capable of being a software access point (SoftAP). There are plenty in the market; just make sure it can broadcast its own network (
Newegg,
Amazon). Download the latest software from the adapter's manufacturer and set up a new access point with either WEP or no security. Plug it in when you want to DS WiFi; take it out when you don't.
That's pretty much it, really.