Insert a Hyperlink into the merge document to give you the Web Address
tooltip, which I am pretty sure is not configurable from the fields. Toggle
the hyperlink field (ALT+F9) and replace the web address with the Mergefield
that contains the web address. Update the field and toggle the display back
again. You should then be able to merge to a new document as previously
suggested.

I think you have to use Word Mail Merge events for this. I have not tested
this recently, but for example:

1. Create a new document, connect it to your data source, and insert one
merge field and a bookmark named "mybm"

2. Open up the VBA Editor and
a. insert a class module.
b. name it EventClassModule in the properties box
c. Copy the following code into the module:

Public WithEvents App As Word.Application

Private Sub App_MailMergeBeforeRecordMerge(BYVal Doc As Document, Cancel As
Boolean)
Dim dt as String
Dim lt as String
Dim h as Hyperlink
Dim r as Range

' set the range variable to our placeholder bookmark
Set r = Doc.Bookmarks("mybm").Range

' delete any existing text (this is needed for records after record 1)
r.Text = ""

' construct the link text that you want. I'm assuming your data source
' has a field called WEBADDRESS for the link. NB, these field names
' are case-sensitive.
lt = Doc.MailMerge.DataSource.DataFields("WEBADDRESS")
' set up the display text that you want. I assuming you have a field
' called WEBTEXT
dt = Doc.MailMerge.DataSource.DataFields("WEBTEXT")

' insert the hyperlink you want
Set h = Doc.Hyperlinks.Add(Anchor:=r, Address=lt, TextToDisplay:=dt)

' Set mybm to "cover" the inserted link so it is easy to delete the old
hyperlink

Doc.Bookmarks.Add Name:="mybm", Range:=h.Range

Set r = Nothing
Set h = Nothing

End Sub

3. Insert an ordinary module (the name does not matter) and insert the
following code:

Dim x As New EventClassModule

Sub autoopen()
Set x.App = Word.Application
End Sub

4. Save and close the document. Open it to trigger the autoopen, then
perform a test merge.

NB, if you start changing the code you may find that you need to re-run your
autoopen code again, and/or save/close/open the document. You should realise
that
once you have enabled the events, they apply to any document until either
you or
Word has disabled them again. This is why I do not particularly like using
Events, but even so,
I suspect that this is the easiest way to perform this particular task in
Word.