Just to confirm you can ask for no stamps on entry. Expect a bit of an inquisition though! I'm there pretty often.
Andy, if you route through Cyprus I can help you - we have a g/a hangar in Pafos under construction. We operate all over the region and can assist you. Pafos - Beirut is very straightforward and a quick flight. Pafos - Egypt is also not too difficult with Alexandria 'just across the water' and a regular destination.