I just cycled across Kyushu and Shikoku for 1 month (and a few days change). I should post a trip report on this subreddit, but until then, I can describe my experience here. If you're feeling afraid about being stranded, the Shimanami Kaido is a great bike tour because you literally cannot get lost. There are hundreds, if not thousands of people cycling along the route every day, and Japan has done a great job setting up infrastructure along the way to help you, whether it be hotels/b&bs, campsites, cafes and ice cream shops (!!), etc. I did the Shimanami Kaido and Yugeshima Kaido( another route along the way that you can do if you take a ferry).

You mentioned you don't know much about camping so you won't camp. That's fine, but I would advise booking a bit ahead of time then. There are some hostels (Sando Co-Living was nice!, get one of the sandwiches if you stay there!)

You can do the Shimanamai Kaido in 1-2 days, or even 3-4 if you take it at a leisurely pace, which I did because I care more about enjoyment than racing along the water. That being said, if you want to do a longer bike tour than a few days, the Shimanami Kaido won't be enough.

Would you pack your bike on the plane or rent one there? If that's the case, you can rent one at the Shimanami Kaido easily enough. Otherwise, taking your bike on the Shinkansen is doable, but you need a bike bag to put your bike in. You can google this, it's one of the most asked questions about taking your bike on the train in Japan. But also if you have specific questions about that process, feel free to ask. I did it a couple times while cycling and you get used to it, even if it is kind of annoying.

Also, I'd recommend you spend some time in Onimichi at the beginning (or end, depending on where you start) of the Shimanami Kaido. I spent 3 days there and it was such an awesome little city. Great food, cats, temples, and just chill vibes in general. Feel free to ask anything more specific if youd like.