You need to extract your emuNAND using the tool and then inject it into the new SD Card. After that, just copy over your files.
Steps using emunand tool:
1. Remove old sd card for the 3ds
2. Insert new SD into 3ds
3. Format emunand on the new SD
4. remove the new SD from the 3ds
Now, the rest of these steps take place on your PC
5. insert Old SD
6. Copy contents to a folder
7. open emunand tool and backup emunand
8. remove old SD and insert the new one
9. copy contents of that folder to the new SD
10. inject the emunand we extracted earlier (using emunand tool)