Hello Mark,
Thanks for writing to us.
Regretfully, there is no option to add custom HTML in the Header. It would require custom development. I would suggest you contact a developer who can assist you with your concern.
Please note that WordPress doesn’t support the SVG media file. Please have a look at the supported media by WordPress https://wordpress.com/support/accepted-filetypes/
To add SVG support on the WordPress media you need to use an extra plugin from WordPress plugin repository or in case if you have an idea about coding you can check this article
Please note that we don’t provide custom development support and any third-party plugin support. It is out of the support scope.
Hope it helps
Thanks for understanding