[Nyororin]

As someone with large feet - and with a husband who has large feet... I can tell you it is going to be a pain.

The best suggestions I can make;

Confirm your shoe size. Stand on a piece of paper and trace around your foot. Measure from the tip of your big toe to the heel. Then measure around the front of the foot at the base of the toes. (wrap the measuring tape around your foot.)
With these measurements, in cm, you can check which shoes you can fit into. This is REALLY important.

An example - All the shoes I wore in the US had the cm size of 27 or 27.5 on them. For years I assumed that since they fit me well, my cm size was 27 or 27.5. As that size is about as rare as it can be without not existing at all in Japan, I NEVER bought shoes here. Never even tried, as it was a guarantee that the size wasn`t made on any shoe that I would wear. I`d stock up on shoes in the US.
Then, one day, I actually bothered to measure my feet.
My feet are 25.5 cm long... Which means I would actually wear a 25.5 in Japanese sizes. That size, while still a little more common, is pretty hard to find too.... 25s are easier, and 24.5s are everywhere. My foot is too long to fit into either of those, *unless* they are wide sizes. A wide 25 actually has up to 26 in length, and a wide 24.5 has up to 25.5. My feet are normal width, so some designs (like heels and flats - anything that is slip-on) won`t work in wide, but anything casual or with straps or laces will.
While still not exactly *everywhere*, 24.5W are not all that hard to find. Any larger shoe store will have a wide selection.

My husband was also able to find that he could fit into a much smaller size than he had originally thought. In his case, his feet are wide, so he was choosing a size that fit him in width, which was pushing his size up drastically.

However.... With your size, I`ll be honest and say that it is going to be HARD. Even if you could fit in a smaller size with the width measurements... It isn`t going to take you down to a common size. You might get lucky and find a few places that have one or two styles available (likely for order), you`re not going to have an easy time at it. The largest size I have ever seen in mens shoes, even in specialty shops, is 30.5. Your listed size is considerably larger.
I would just stock up before coming to Japan, because you`re not going to find much here.