The easiest way to transfer a workspace to a new PC is to ensure that the original sonar log files are stored in the same relative path on the new PC. e.g. if sonar logs are in C:\SonarLogs then make the same directory and copy the logs there. Then just copy each workspace folder over, including all contents.
Note that original sonar logs are only required for the sonar viewer and sidescan mosaic - all depth data is stored in the .rmdb database file, so if you just need mapping then you actually don't need to copy the log files over - but you will get a warning message each time you try to open a track edit window.