Just an idea:

1. Make a user called ‘Guest’ and look up the user ID
2. When redirecting your potential clients to the admin page, redirect to a script that’s logging in your clients as the guest user (Code #1)
3. Add an WordPress action to disallow the user when logged in as ‘Guest’ and not on customize.php (Code #2)

Code #1

$creds = array(
    'user_login' => 'guest_user',
    'user_password' => 'guest_user_plain_password'
);

$user = wp_signon( $creds, false );

if ( is_wp_error( $user ) )
    echo $user->get_error_message();
else
    wp_redirect( 'your_absolute_admin_url' ); exit;

Code #2

add_action( 'init', 'check_guest_user' );

function check_guest_user() {
    // Only when in backend and the guest user is logged in
    if ( is_admin() && user_id = get_current_user_id() ) {
        // Block other pages then custom.php
        global $pagenow;

        if ( 'customize' != $pagenow )
            exit();
    }
}

// replace user_id with the user ID of 'Guest'

Only problem with this script is when multiple users are trying the customizer. Saving customization settings per user would make things a lot harder.

It answers your question though, as it is a solution to give access to users to a specific page without them having to register an account.

http://codex.wordpress.org/Function_Reference/wp_signon