How do I intercept query table errors, bypassing the Excel ones?

Here's an example of what I'm trying to do using examples from the Help
files:
Sub Macro2()
Workbooks(1).Activate
Application.DisplayAlerts = False ' This doesn't make a difference for my
purposes
On Error GoTo ErrorHandler
Selection.QueryTable.Refresh BackgroundQuery:=False
GoTo Exit_Sub

ErrorHandler:
Msg = "Error # " & Str(Err.Number) & " was generated by " & Err.Source &
Chr(13) & Err.Description
MsgBox Msg, , "Error", Err.HelpFile, Err.HelpContext

Exit_Sub:
On Error Resume Next
Application.DisplayAlerts = True
End Sub

For testing I've moved the database to a different folder so the first error
window is "Please Enter MS JET OLE DB Initialization Information", then my
example message box. I want to COMPLETELY bypass the Windows error window
and just use mine.

Suggestions?