Preparing Luigi's Mansion 3DS for resale

I'm considering selling my old blue 3DS to help fund a New 3DS. The 3DS I bought was the one that came bundled with Luigi's Mansion (an uninspired move on my part) and I want to remove my personal data from the console without deleting that game, to add to the value.

My question is: is this possible? Or when I registered my NNID with the console did I eliminate any chance of this working out?

This is not possible. When you set up a NNID on your system, the digital copy of Luigi's Mansion was linked to it. You can see this by deleting the game from your system, going to the eShop, and checking redownloadable software - Luigi's Mansion will be there. You can delete a NNID from a 3DS system, but it will also make any linked games unplayable, which would include Luigi's Mansion.

Your options here are to either sell the system as is with your NNID attached and then create a new one on your new system (not optimal if you want to keep your Mii, friend list, StreetPass data, or any of your other downloads), or perform a System Transfer, thus transferring Luigi's Mansion along with it.