These wood steering wheels were probably factory addembled with old style hide glue, which is moisture sensitive. Pushing some good grade wood glue into the cracks would help, beyyer would be to slide a thin knife along the crack to open it up a bit before gluing. If the whole piece comes off, all the better. Wood glue, careful alignment with the other parts, and clamp. It will last for ages.
When I was assembling my '29 limo from a near scrap yard rescue, several of the outer layers of the wheel were loose. Glued them with Weldwood, they are still tight after 50+ years. The hazard with epoxy is that it is Permanent. If you need to repair something down the road, an epoxy glued joint can not be separated.