You may try doing this by applying archival logs in Mysql which is called as binary logs. Have your instance my.cnf in the below manner under [mysqld].
--binlog-do-db=A
--binlog_format=statement
Restart mysqld.
Every four hours let cron to exec a script by doing below steps one by one.
1). "flush logs" on the server. Get file names from binary logs generated from restart to latest - 1. (Make a note of latest - 1 file name for later reuse).
2). Convert those logs to .sql .ie., mysqlbinlog mysql.0000021 > mysql.0000021.sql ; mysqlbinlog mysql.0000022 > mysql.0000022.sql ... so on until latest - 1.
3). Now replace string "use A" to "use B" like. sed -i 's/use A/use B/g' mysql.0000021.sql
4). Now apply them to your DB instance.
mysql -uwill -psmith << EOF
source mysql.0000021.sql ;
EOF
5). Capture errors in the below manner at the starting of the script.
exec 7>&2
exec 2> ERR_FILENAME.txt
6). And now if [ -s ERR_FILENAME.txt ] then sendmail ; fi
7). For the next iteration use the binary log file that you took a note at step 1 as a starting file name.
IMPORTANT
Ensure user "will" doesn't have any permissions to update database "A". It should be explicit to "B". By chance even if you forget to replace, it won't change.
First try this in your test environment try all your application functionality that are properly replicating without any goofups. There you go and no need to call a guy ;)