cPanel user account has a privileges to control all created databases under cPanel account, And because phpMyAdmin in cPanel is using cPanel authentication you are automatically redirected to the phpMyAdmin control page without asking for login info.
Your target could be done with changing cPanel password without changing mysql user password.
You can do the following steps :
1 - Create MySQL user and add this user to database with full privs.
2 - Create new cPanel account Login through new account Change new cpanel
3 - user password through "Change Password" And un-check Allow MySQL
password change.
4 - Click phpMyAdmin from the new cpanel account and you
will be asked for login info
5- Type the login info of the created mysql
user in step1.
You can now login to the required database without old account cPanel info.
There is another soln is to copy /usr/local/cpanel/base/3rdparty/phpMyAdmin to /usr/local/apache/htdocs and login through http://ip/phpMyAdmin
Don't forget to change the auth_type in /usr/local/apache/htdocs/phpMyAdmin/config.inc.php to http or cookie