Can I remove the middle slave in a MySQL "master -> slave -> slave" setup?
Add additonal step to avoid any confusion you could do flush tables with read lock after replication is caught up as it will do global lock and would avoid conflict in case of any change coming up, use unlock tables at the end to release the lock acquired. Moreover it would be better to have this done in low/off production time in case it is in production, other steps seems to fine

Hope it helps.