amda2008

If you have access to phpmyadmin, then you can set different theme (like twentyeleve theme).
Access database, click wp-options, you will find template and stylesheet rows in seconds page. Change it to any theme that is present in your installation.

Since you have only 2 sites, then it would be better you try separate installation for each site.
Point the domains to separate folders and install.

People will be accessing your old website until you point your DNS records to your new server.

Assistance