The only sd I have that is big enough is the one I am currently using. Would it work if I used emunandtool to back up the current emunand and reload the old emunand, and when I back the saves up restore the new emunand?
Yes it should work, but just in case also make a backup of your SD card frequently!
You should check in your Nintendo folder which emunand belongs to which folder.You should have at least 3 folders in there now. 1 for your sysnand 2 for your emunands. I suggest you backup the Nintendo folder on your pc to check which 1 is for your sysnand 1st by deleting your folder & booting up your system in sysnand only, after that close system & remove the SD & check in the Nintendo folder what folders are in it & note them down/make prnt screen.
After that boot emunand repeat what you did before, no need to delete Nintendo folder.
Now you should've figured out which folder belongs to which emunand so you can delete the Nintendo folder on your SD & copy only the folders you need for your sysnand & emunand & this way you can separate the emunands for use on a different SD, to simply just save space on your SD card or if you only want to use your sysnand folder without emunand saves!
I hope this helps you to keep things a bit organised in the future.