I don't really understand the purpose of calling Application.GetSaveAsFilename() since you are going to override the filepath they choose? If it's to give them an opportunity to cancel the process then you could use a message box?
Not tested, but I think you might be looking for something along the lines of...
Private Sub CommandButton2_Click()
Const sLOG As String = "Shift Hand Off Notes - "
Const sFILEFILTER As String = "Excel files (*.xls),*.xls"
Dim sInitialFileName As String
Selection.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks _
ActiveSheet.Protect DrawingObjects:=True, Contents:=True, Scenarios:=True
sInitialFileName = sLOG & Worksheets("Hand-off Notes").Range("K1").Value & " - " & Worksheets("Hand-off Notes").Range("F2").Value & " - " & FormatDateTime(Date, vbLongDate)
If MsgBox("Do you want to save and e-mail the Shift Hand Off Notes?", vbOKCancel, "Continue?") Then
ActiveWorkbook.SaveAs Filename:="S:\share\dc\LP\LP Hand-off\DC 840\" & sInitialFileName
MsgBox "Email sent"
MsgBox "Process cancelled"