As you have seen, if you have WebLink set up to automatically log in, users cannot manually enter credentials.
To allow users to change to manual login, you could add an additional Repository Connection to the same repository using Windows Authentication, but leave the "Automatically log in" box unchecked. Users can then logout, select the manual login repository, and enter their credentials. Make sure you have different Display Names for the two connections to the same repository, like "YourRepoName - automatic login" and "YourRepoName - manual login" so that the users can tell which repository to select.
If you leave the default DBID (database ID) unchanged, then users who only want to use automatic login will not see any changes.
Edit: as Wes and Farzali have noted below, to see the selector you must have "no default" selected, which means that users will always have to select a database to login. It is possible to change the CSS file for WebLink to change this behavior.