Dying at 60 is old in feudal Japan, and dying of cancer isn't weird in any way for a presumably otherwise strong, healthy person, so that part of your line of reasoning is fatally flawed.
As for the exact cause of death, I don't know and can't read the primary sources, so I can't help you much there. I can make an educated guess based on general knowledge of how our knowledge of history is put together, though.
Either there are conflicting sources, I'm which case we can speculate on which of the are more likely to be true, or we have one source which is interpretent in different ways. In either case, unless a cause of death is very obvious (e.g. decapitation), we will seldom be able to make a definite diagnosis based on the source.
I'd be interested to hear if you find any good sources, but I'm plenty happy assuming that he got sick and died at an old age like a lot of the people through the worlds history, and that the exact sickness is a little unclear like most of the people through the worlds history. After all, the same thing can be said of most historical figures until relatively recently.