JP, yours does look in really good condition, maybe just the old varnish cracking or worn away. In your photo I can see at least one spot where it is gone and there is some staining of the wood. That may take some work. Gorilla Glue is really good stuff for any cracks but, as Doc suggested, you do have to clamp it well without denting the wood. I can't tell for sure what wood you have there but it looks like probably mahogany. Depending on the variety, it can be fairly soft.
I would be a little leary of an oil finish. Changes in humidity, combined with hand grime over time, could really make for a sticky mess. Besides, it will never be a "permanent" finish. Regular cleaning and reapplication will be required.
Doc, did you find an epoxy with a UV inhibitor in it? I understand that most are not suitable for final finish where exposed to sunlight unless covered by spar varnish or automotive clear or something else with UV protection. I have to say that whatever you did, that's a quite handsome wheel there.