You can easily back up your current Big Cartel theme from your admin area. Your back up will be downloaded to your computer hard drive and will include all customisations you have made to your CSS and theme files (including custom option settings on an Aarcade theme) as well as your custom pages.
Backing up your theme
In your Big Cartel shop admin area, click the Customize design link at the top right of your Big Cartel admin area:
Click the Advanced icon and then click the Download current theme link:
Your theme package will be downloaded to your preferred location on your computer’s hard drive. This is typically your Desktop or Downloads folder.
Using your back up file
Refer to How do I uninstall a theme or restore a backed up theme? or you can open specific files in your backed up theme - in your preferred HTML editor - and reference your old theme customisation and settings as needed.