Something like this (but notice it won't deal with nested fields), and unless you change Word preferences, Word will re-insert the links when you start editing the results:
Sub replaceHLs()
Dim hl As Word.Hyperlink
Dim i As Integer
Dim r As Word.Range
Dim strLinkText As String
For i = ActiveDocument.Hyperlinks.Count To 1 Step -1
With ActiveDocument.Hyperlinks(i)
Set r = .Range
strLinkText = .Address
' optional, should be OK for HTML links
If .SubAddress <> "" Then
strLinkText = strLinkText & "#" & .SubAddress
End If
r.Text = strLinkText
r.Font.Color = wdColorBlue
r.Font.Underline = wdUnderlineSingle
Set r = Nothing
End With
Next
End Sub