You could try saving them as part of a themepack, but I don't believe the themes compress and store cursors internally the way they do with wallpapers. Unfortunately the only way I know to do what you want is to export out of the registry, but that would only work if the new computer had the cursor files stored in the exact same path.
If this was helpful, please vote by clicking the green triangle. If it solves the issue, click Propose as Answer. Thanks!