While your SQL query will probably do the trick, you don't need to interface directly with the database to accomplish this.
The preferred methods would by using Wordpress' update_option() function or by running the WP-CLI command:wp option update.
To override the admin email change confirmation process, add the following to your functions....
Not a great idea in my opinion.
You could, of course, resort to some voodoo, filter the query or do some magic in HyperDB or MySQL Proxy, etc., but that's just going to be so fragile. You haven't specified why you want to query products from another database, so I'm going to assume you just want to shard it for scalability.
When doing any kind of sharding ...