After further Googling I was able to come across a site that explains how to achieve this.
The second function on the page is quite helpful. This looks for “ver=” and checks that it matches the WordPress version number and then removes it. The first function on the page removes all version numbers from all files.
The function that achieved the results looks like:
// remove wp version param from any enqueued scripts
function vc_remove_wp_ver_css_js( $src ) {
if ( strpos( $src, 'ver=" . get_bloginfo( "version' ) ) )
$src = remove_query_arg( 'ver', $src );
return $src;
}
add_filter( 'style_loader_src', 'vc_remove_wp_ver_css_js', 9999 );
add_filter( 'script_loader_src', 'vc_remove_wp_ver_css_js', 9999 );