Well, I have made most of an electric guitar thus far with a router… I don’t think a few circles with a rounded profile is particularly intimidating to me.
I would be tempted to cut discs with a drill press and a hole saw, then simply add a rounded profile with the right router bit. But that’s just me. This is essentially two wooden discs attached by a dowel. Not saying I’d have a TMBR-quality throw right off the top, but it’s not rocket surgery!
You could also create a “copy carver” which is just a router and mirroring stylus. For something simple like a yoyo, a copy carver would be overkill, but it would do the job, that’s for sure. Think of it as low-tech CNC, where instead of a program file, you use a physical object as your template.