You could save the file in the compatibility mode of an earlier version that had the links available as described, then replace the path in the field, update the field and save it back in the compatibility mode of the current version. It should work fine provided you have not used any more recent features in the document, such as some content control types applicable only to later versions of Word.
Put the new path where indicated at the top of the macro and run the macro
on a copy of your document.
Code:
Sub ChangeLink()
'Graham Mayor - http://www.gmayor.com - Last updated - 07 Nov 2018
Const NewPath As String = "C:\\Path\\"
Dim oFld As Field
Dim strCode As String
Dim vName As Variant
ActiveDocument.SaveAs2 FileName:=ActiveDocument.FullName, CompatibilityMode:=11
For Each oFld In ActiveDocument.Fields
If oFld.Type = wdFieldIncludePicture Then
vName = Split(oFld.Code, "\\")
strCode = " INCLUDEPICTURE " & Chr(34) & NewPath & vName(UBound(vName))
oFld.Code.Text = strCode
oFld.Update
End If
ActiveDocument.SaveAs2 FileName:=ActiveDocument.FullName, CompatibilityMode:=Val(Application.Version)
Next oFld
lbl_Exit:
Set oFld = Nothing
Exit Sub
End Sub