If the database has no data that you need to preserve the easiest method is just to install the app on the new host and set the connection string to your new database on the host. On the first attempt to load a page accessing the database, the database will automatically be created (note that you need to load a page which hits the database - sometimes the home page is not sufficient). This method is a lot more straightforward than generating SQL and then executing it on the production database.
If there is data that you need to preserve then the best method will be taking a backup and installing the backup on the host. In SSMS simply right-click the database in the left pane, then Tools > Backup... To restore on the server connect to the server in SSMS and right-click the 'Database' node in the left panel and select 'Restore Database...' I'm not sure if the host provides a direct connection from SSMS but they should at a minimum have a mechanism to restore a .bak file.
Going forward you should ensure that you can execute SQL on your database as a very convenient method for deploying EF Migrations is to generate the SQL update script on the development server and then deploy this by executing it in production.