Your code as posted creates a message for each account? However you could edit the message to remove the signature. In the line
Rng.moveStart 4, -3
change the -3 as required to remove the appropriate number of paragraph from the end of the message.
'Opens Email Disclosure Template
Sub OpenEmailTemplate()
Dim oAccount As Outlook.Account
Dim olInsp As Outlook.Inspector
Dim wdDoc As Object
Dim oRng As Object
Dim oTemp As MailItem
For Each oAccount In Application.Session.Accounts
' If oAccount = "testATtest.com" Then
Set oTemp = Application.CreateItemFromTemplate("file path here")
With oTemp
.SentOnBehalfOfName = "sendATtest.com"
.Subject = "PERSONAL AND CONFIDENTIAL COMMUNICATION"
Set olInsp = .GetInspector
Set wdDoc = olInsp.WordEditor
Set oRng = wdDoc.Range
oRng.collapse 0
oRng.moveStart 4, -3
oRng.Delete
.Display
End With
'Exit For
'End If
Next
Set oTemp = Nothing
Set oAccount = Nothing
Set wdDoc = Nothing
Set oRng = Nothing
End Sub