I don't know how your SQL Server is set up but if you can authenticate the client application with the SQL Server via Windows Authentication then this would be the ideal solution concidering you won't be exposing a username and password.
A connection string of this type would be something similiar to:
[This would work for ASP.NET C#]
conn.ConnectionString = "Data Source=YourServer;Initial Catalog=YourDB;Integrated Security=SSPI";
You show: Integrated Security=SSPI in your connection string already. Thats windows authentication. You won't need to supply a user or password with that enabled. You will just need to make sure the client can communicate with the server through windows authentication.