Is a CiviVolunteer shortcode available?
No, there is not a shortcode available, but I'm not sure either that it isn't trivial to enable one.

But, I suspect it is not necessary for what you are trying to acomplish.

Have you enabled clean URL's for your CiviCRM install?

https://docs.civicrm.org/sysadmin/en/latest/install/wordpress/#enabling-cleaner-urls-for-wordpress

After you do that, the sign-up page should be displayed with your wordpress front-end theme: http://example.org/civicrm/vol/#/volunteer/opportunities

Be sure to note the permissions required: https://docs.civicrm.org/volunteer/en/latest/sign-up-form/

I think this would enable your custom plugin to display its headers.

Saludos!