Update Via API Call?

We use a cloning plugin (NS Cloner) that works well, but doesn’t update the URLs. We would like to hook our update process into the update URLs e.g.
update_urls($site_id, 'old-phrase', 'new-phrase');

Can you advise it this is possible?
Happy to wrap in a custom function e.g. switching to the blog, then calling the method.

Thanks in advance,
Alex Furr