Hi,
I have been AI to both Turkey and Egypt and highly recommend either, I would say Egypt for weather purposes in late Sep or Oct as Turkey bit more chance of rain. Can't say about singles though, i'd try a specialist singles company. Be careful though as both countries notorious for hassle, Egypt prob slightly worse. If you happy to stay in your resort (they are all huge) you will not have to worry.
Depending on your finances, I recommend El Gouna, its a private resort and absolutely fabulous, you will not be hassled there. Google it if you fancy.
Have a fab time where ever you decide x