If you have TAC support, they will certainly walk you through the process. If not, here are some high level suggestions. Copy the startup configuration and the vlan.dat file to the storage media (CF, SD card, whatever) where the IOS resides. Replace the SUP with the new one with the old storage media. Copy the file to the new startup config, and copy the vlan.dat to wherever it resided before (most likely bootflash:). Then reboot the switch and you should be good to go. Obviously there will be down time in this. I would suggest you give yourself no less than 2 hours. It could be less, but try not to paint yourself into a corner!
The supervisor card is VS-SUP2T-10G
Look at the front of the line card: Left side there is a CF slot & right side there is a USB port.
Either way, the IOS, config and VLAN.dat can be exported/imported through those media.
I think the CF slot is called "disk0:" and the USB slot is called "USB0:".