Exactly. If you can format the SDCard on your computer, you can copy the date from the card to the computer and from the computer back to the new card without using your phone.
Transferring over wireless will be slower than direct physical transfer. For someone upgrading a 16 GB SDCard to a 32 GB SDCard, it's a pretty good bet that they have a god bit of data that needs transferring.
Glad you got it all working, WK.