Frankly it would be better if you associated signatures with your accounts and then they are included when you create messages, however with some provisos the following should work, Change the signature as appropriate and test with a small number of messages in drafts,

Public Sub AddSignature()
'Graham Mayor - https://www.gmayor.com - Last updated - 11 Apr 2021
Dim FSO As Object, oSig As Object
Dim olItem As MailItem
Dim strPath As String
Dim strSignature As String
Const strSig As String = "Graham Mayor.htm"    'the signature to add - change as required

    strPath = Environ("appdata") & "\Microsoft\Signatures\"
    Set FSO = CreateObject("Scripting.FileSystemObject")
    Set oSig = FSO.OpenTextFile(strPath & strSig)
    strSignature = oSig.ReadAll
    oSig.Close

    For Each olItem In Session.GetDefaultFolder(olFolderDrafts).items
        If TypeName(olItem) = "MailItem" Then
            With olItem
                .BodyFormat = olFormatHTML
                .HTMLBody = .HTMLBody & strSignature
                .Display
                '.Save
            End With
        End If
    Next olItem
lbl_Exit:
    Set FSO = Nothing
    Set olItem = Nothing
    Set oSig = Nothing
    Exit Sub
End Sub