If they refuse to give the website details so what you can do is tell them to do the changes. As I'm also an SEO Expert I understand these so my advice is either you take complete control of the website by transferring to your account or give the required changes details to them and ask him to do it for you.
Of course he will demand some amount of money but that's the only way.
Please give it a +1 and also click "Mark As Accepted Solution" if you find it satisfactory. Thanking You With Regards | Harry Parmar