1. Octopus legs should be sliced from the left (for the right hander), which is called sogigiri (そぎ切り). You can see how it is done in my post Sashimi. See note 4 about how to boil octopus.
2. It would be a challenge to slice cucumbers into such thin slices unless you are good with knife. I use the Kyocera brand slicer that I introduced in my post Lotus Root and Mizuna Salad.
3. If you have a bit of time, then I’d suggest that you chill the sunomono in the fridge for a while. It tastes better in my view.
4. To boil a whole octopus:
a. Bring water in a large pot to a boil. Add a pinch of salt and a dash of vinegar.
b. Hold the top of the octopus (the round part, which is actually the body) and dip most of the legs in the boiling water. Move them up and down like yo-yo until the legs are nicely curled.
c. Drop the entire octopus into the boiling water.
d. Cook for about 4-5 minutes then turn off the heat.
e. Leave the octopus in the hot water for another 5-6 minutes but no more than 10 minutes from the time you dropped the entire octopus in the boiling water.
f. Take it out and cool it down.