@Cyclo I have traveled quite a bit since completing my breast cancer treatment 3 years ago and each time I have had insurance for everything EXCEPT my cancer.
It has changed the way I book my trips as I now try to pay small deposits (that I am willing to lose) or else I book things that I can cancel and get a refund. I haven't done a really long trip (previously I have traveled for 10 to 12 weeks at a time) and my longest trip post BC has been 18 days. I get to a month or so before my trip (visit my doctor or have scans if they're due) and then decide I'm definitely going and then I pay for everything and I just go. I figure if something happens while I'm away I will either wait until I return or I will fly home.
Realistically a recurrence does not typically make you sick right away - the main risk is the possible delay in treatment. Think back to when you were initially diagnosed - you probably felt fine and were going about your normal life until the diagnosis hit you.
One thing I did clarify with my insurance is that I would be covered for DVT - as I was on Tamoxifen initially (which increases the risk of DVT) I didn't want them to say it was linked to my BC and therefore not covered. I received confirmation (in writing) that as I did not have DVT currently I would be covered even though I was at higher risk.
Next February I am traveling to South America and Antarctica!!!!! For this trip (which will be over a month) I had to get insurance that would cover my breast cancer. It was ridiculously expensive (but if you're going to Antarctica EVERYTHING is expensive!) At the time of booking I was 2 years since completing my treatment. I needed pathology and oncologist reports as they wanted stage and grade and wait to see if I would be covered.
Good luck and enjoy your trip to Japan - I just got back a few weeks ago and it was brilliant!