You should create a login on your primary, create a corresponding user in log shipped database and wait until this user "flows" on your secondary, at this point you can drop the login on primary.
If you use windows authentication, you've done. If you use SQL Server authentication, memorize the sid of the newly created login before you drop it, on your secondary you shoul recreate the login using this sid, the sintax is:

    create login yourLogin with password = 'yourPassword', sid = 0xC10434A5BE32CE4E85EA71E6B04C068F -- the sid assigned to tle login on primary