How to set a different theme when the site is on maintenaince mode?
I think there is no way to set active theme while on maintenance mode, but you can change the way site looks.

For that to happen in your local site there is /modules/system/maintenance-page.tpl.php available. 

You can overwrite as you need by pasting this into your theme directory.

Then in settings.php you need to set 

$conf['maintenance_theme'] = 'ThemeName'