It's wupinstaller. WUDs are disc images.
You do need signature patching to install un-owned DLC or to run a game on which you've installed un-owned DLC.
So do this...
...or, if you only have a couple games that it applies to, just run it (once per bootup) before you run one of those. If you forget, you'll just get a message that your DLC is corrupt. Cancel that, run Mocha, and you're good.
...or, as you're saying below, go with Haxchi. Please don't jump right into CBHC until you're comfortable with what you're doing. It's only one extra click to start Haxchi manually.
No, you don't need to remove anything. The browser exploit is only temporary anyway. It doesn't change your system. Also, you'll need to use the browser exploit to start HBL to run the Haxchi Installer.
Side note: Keep in mind that you have to legitimately buy one of the compatible DS games from eShop in order to use Haxchi as it was intended. (some people try to use a fake-signed downloaded copy) Using the browser hack to load Mocha, as Mr Objection suggests is free. (but you need an active network connection for that)
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Yes, you can transfer wupinstalled content as you would eshop content.