I need a query to move a record from one table to another without using multiple statements?
There is no way to make it a single query, but if you HAVE to do it in a single query within an application you can create a Stored Procedure to do it for you.
DELIMITER $$
DROP PROCEDURE IF EXISTS `copydelete` $$
CREATE PROCEDURE `copydelete` (id INT)
BEGIN
INSERT INTO New_Table SELECT * from Old_Table WHERE Old_Table.IdField=id;
DELETE FROM Old_Table where IdField=id;
END $$
DELIMITER ;
Then you're new query is just
CALL copydelete(4);
Which will delete WHERE IdField=4;