I live in Greece now. The houseflies are bad here too.
Even with all the torn screens replaced they find ways to get in, and too many don't get drawn into the zapper which is constantly going.
Obviously a fly swatter is going to work better than your hand because you can flick your wrist a lot faster than moving your entire arm.
However if the flyswatter isn't handy because I left it the last place I sat before I moved to my favorite chair, I've found the following technique is good and nets about a 75% kill probability.
Observe the fly after it lands on you. Watch it as it crawls around and then usually settles into one spot and does this thing where it seems to be licking it's feet. At this point it's the least aware of it's surroundings and its guard is down. It's still gonna be quick and it's got like 100 eyes looking everywhere, but as you observe it your hand is slooowwwwly creeping up so it's within about 1 foot of striking range. Then, when the fly least expects it you bring that hand straight down with no hesitation and no pulling back. Sure it's gonna sting a bit at the impact point but it won't last and this requires 100% commitment. There's little satisfaction in life greater than that feeling you get when you lift your hand and the crumbled mess of what used to be a fly rolls off your arm or leg.