Do I need to redesign my Database and get rid of foreign keys for successful replication?
This looks like a non-issue, because, obviously, you will be using the same table definitions, including engine, on both servers. The example in the MariaDB Knowledge Base article you linked to has different storage engines: the slave server doesn't have InnoDB, so it defaults to MyISAM, which doesn't support foreign keys. MyISAM does tolerate foreign key constraints in the CREATE TABLE statements, but it silently ignores them, so any defined cascading deletes will not happen.