First up... YOU'RE OK for the SDHC card size! 32 GB is the maximum limit for SDHC (SD High Capacity, utilize FAT32 format) cards, as 64 GB & higher are SDXC (SD eXtreme Capacity) that utilizes exFAT (aka FAT64) format which isn't supported by the 3DS at this time.
Second, if you don't mind "retiring" your old SD card in your 3DS... just do a simple copy of all the data on the old SD card to your computer (consider it as "backing up" that card), then copy all that data to the new SD card. Just make sure the folder structure is exactly the same when copying to the new SD/HC card to ensure that your 3DS will find the files. If the files on your system gets corrupted, you can always go back to the original SD card & re-copy the files.
Third, the SD/HC card might cause some delay when starting up your 3DS as the system will need some time to read the SD/HC card, so those games will be temporarily unavailable for a few seconds. DON'T PANIC! They'll appear where you placed them once the system finds the data on the card. This delay might get longer as you add more stuff to the SD card (I have ~30-40 digital titles on my card), but it's one evil that you'll have to live with ONLY when starting from a complete power down. Playing games off the SD card will remain unaffected.
I've done a similar thing with my 3DS, upgrading from a 2 GB SD card to an 8 GB SDHC card without losing any data. What you're planning on doing is just a larger jump than what I did, so things should turn out the same.
Hope this helps!