How to "swap" out production tables
You can do swapsies by specifying both tables in your RENAME statement. 

CREATE TABLE new_table (...);
RENAME TABLE old_table TO backup_table, new_table TO old_table;


MySQL documentation on RENAME TABLE says:


  The rename operation is done atomically, which means that no other session can access any of the tables while the rename is running. For example, if you have an existing table old_table, you can create another table new_table that has the same structure but is empty, and then replace the existing table with the empty one...