Staying in Fatih, dress code?

Hi I'll be staying in Fatih during summer, topkapi area.

I'm worried about the dress code,

and what's safe to wear,

has anyone been/know much about this area and if I have to dress really conservatively,

It's going to be above 30°c so I'd love to be able to wear short clothes but would rather be safe and not stand out if there's a dress code for this area. TIA :)