I have run my phone without the card, so I don't think it has too much on there that is absolutely necessary. I did notice without it in, it would not take pictures.
I think what he means by offline is not in the phone. Personally I would just hook up your phone to your computer and mount the phone as drive and copy and paste all the contents on to your computer. Then install the new SD card and see if it asks for the new card to be formatted by the phone and let it do the rest. Then you can copy your personal files from your computer to the new card. Good luck!