It's been a while since I've PBEMed but the use of Undo was always by exception and with an explanation. Undo's are recorded in the playback; so unless he's equally new or not paying attention your opponent will know if you're abusing the feature. If you're playing a veteran, I'd expect pointed questions when he sees your turn playback. My advise would be to come clean and apologize in advance.
Did you ever see history portrayed as an old man ... weighing all things in the balance of reason?
Is not [it] an eternal, imploring maiden, full of fire, with a burning heart and flaming soul, humanly warm and humanly beautiful?