Instead of having to open and send drafts one by one, add this code to a new module (start with pressing 'Alt'+'F11'), then assign the 'SendSelectedMail' macro to a button on the toolbar.

Public Sub SendSelectedMail()
Dim Sel As Outlook.Selection
Dim obj As Object
Dim i&

Set Sel = Application.ActiveExplorer.Selection
For i=1 to Sel.Count
Set obj = Sel(i)
If TypeOf obj Is Outlook.MailItem Then
obj.Send
End If
Next
End Sub

Gold.

With thanks to Michael Bauer (here).