Yes, it is safe to use third party tools for the Gmail Backup into Another Gmail with Labels. You should try
eSoftTools Gmail Backup Software for this work. They have some very useful advanced features like- Save Gmail Email to Separate File, Export Selective Gmail Account Folders, Download Mailbox with Complete Info, Manually Choose Saving Location, Extract Gmail Emails Date-wise, Compatible With All Windows Editions, Maintain Email Structure & Formatting while transmit the mail from Gmail. They also give a 30 Days Money Back Guarantee and for beginners they offer a Free Demo Trial by which to learn more about software and the service.
Read more:- Exporting Gmail Email to Another with Labels