How can I setup custom templates for a meta-data query

There’s the core function add_*/get_query_arg() that you can use to append stuff to the query and retrieve it.

So simply add a link somewhere, that points to your custom post types single.php template

single-{$custom_post_type}.php

Then append the query arg which would be ?wpse_meta_key=wpse_some_val and then do a switch on top of your template:

if ( 'wpse_some_val' === get_query_arg( 'wpse_meta_key' ) )
{
    get_template_part( 'special_query_template' );
}
else
{
    // do default stuff
}