Modify parent's and child's foreign key value of a record

Question

Consider following relationship on MySQL database.

+--------------+                   +---------------+
|     Child    |                   |    Parent     |
+--------------+                 1 +---------------+
| child_id (PK)| 1           |-----| parent_id (PK)|
| parent_id(FK)|-------------|     | name          |
| name         |                   | address       |
| age          |                   +---------------+
| gender       |                  
| grade        |
+--------------+

I want to update a record where parent_id = 100. My requirement is to modify to parent_id=101. Assume there is no records as 101. This operation need to update child.parent_id = 101 as well so the original relation remains.

My current approach is, roughly

START TRANSACTION;
SET FOREIGN_KEY_CHECKS = 0;
UPDATE Child SET parent_id=101 WHERE parent_id=100;
UPDATE Parent SET parent_id=101 WHERE parent_id=100;
SET FOREIGN_KEY_CHECKS = 1;
COMMIT;

• Can this be problematic in production environment where thousands of writes per second done?
• Is there a proper way I can achieve this without disabling foreign key checks?