Next year Ramadan is from early May to early June. I would not expect Ramadan itself to affect the tour. At the end of Ramadan, there is a huge 3-day holiday which would be June 4-7. Here's a list of the Turkish holidays in 2019. My tour included Republic Day in Ankara. It meant a slight adjustment in that day's schedule but was very interesting to see. I was there from late October to early November, and I thought the weather was perfect. Sometimes I needed a jacket, usually in the early mornings and sometimes in the evenings. I wore summer clothes most of the time. I would have worn sandals more but sturdy walking/hiking shoes are best for most days.
My advice - there's practically no time in Istanbul. Plan to spend at least a couple days there pre-tour, especially if you're coming off a long-haul flight, and/or 2-3 days post-tour. Get in good shape for lots of walking (well, that's pretty much any tour :-). The balloon ride in Cappadocia was wonderful, well worth losing half a night's sleep and a lot of $$$. If you need coffee in the morning to get you started, bring some with you. At least in Cappadocia (3N) coffee was unavailable at breakfast, but I'm sure you can get hot water if you have your own. BTW it's easier to get beer than coffee in Muslim Turkey! The typical Turk has a tiny cup of Turkish coffee once or twice a day; the ubiquitous drink is tea, very strong and sweet.