You can do this via settings import/export. Just note that it would only work if say all your files on the new machine uses the same path as the the old machine.
Go to settings->export settings. Pick a folder where all settings will be exported to. This will produce 3 files (global.ini, canvas.ini, books.ini). The books.ini includes all your read status. On your new machine go to settings->import, and it'll prompt for each of the files in order. As long as the drive path to the files are the same as before, it'll restore your read status for the corresponding files. If you don't want to restore global or canvas settings just cancel when it prompts you and only select books.ini.
Go to settings->export settings. Pick a folder where all settings will be exported to. This will produce 3 files (global.ini, canvas.ini, books.ini). The books.ini includes all your read status. On your new machine go to settings->import, and it'll prompt for each of the files in order. As long as the drive path to the files are the same as before, it'll restore your read status for the corresponding files. If you don't want to restore global or canvas settings just cancel when it prompts you and only select books.ini.