Is it possible to make an arched rabbet, dado or a groove without an electric router? Well.. two years ago I experimented with a hand tool technique that allowed me to create all the above and more. I discovered (although I speculate that others might have figured this out too) that by using a flexible Japanese saw arched against a template, one can cut an arched kerf. This technique can be helpful with shaping wood or producing joinery that requires a round shoulder. But it can also come in handy when you want to decorate a board with curvature geometry. Think about the lid of a box or a panel of a door. The curved kerfs can later be filled with colorful epoxy or veneer of matching thickness.
To make a curved dado or rabbet, all you need to do is to make a template (I used a convex one but a concave template might work too) of the intended curvature, flex a Japanese saw against it and saw down to the desired depth. Then, excavate the wood with a manual router plane or a chisel.
Making decorative epoxies in your work is the same process.