It is a bit of a cheat but if you collect the SID's from the Logins on your Prod Server and create corresponding SID's on the non-Prod server whenever you refresh your database the DB users will sync with the Server logins.
You can do this when you script the creation of your logins.
To get the SID's, SELECT name, SID from sys.syslogins;
To script the creation at the other end
CREATE LOGIN [blah] WITH PASSWORD = N'some password', SID=0xblahblah; You can add other options in there as well like default database, language, expiry etc.
You would only need to do this once and there woudl be no extra steps in your refresh scripts.
You would however need to keep up to date in what logins ou have in Prod as nothing would get done automatically.