@Nachti The provided code unlinks the hyperlink fields in footnotes, i.e. replaces hyperlink with simple text. See the attached input and result document: in.docx (16.1 KB) out.docx (11.9 KB)
If your goal is to change formatting of the hyperlink, you can simply change formatting of the Hyperlink style:
Document doc = new Document(@"C:\Temp\in.docx");
doc.Styles[StyleIdentifier.Hyperlink].Font.Underline = Underline.None;
doc.Save(@"C:\Temp\out_style.docx");