Let me first say that if it was me, I'd replace it.
However, replacing it isn't really necessary for the use you plan for your boat right now. In an emergency, you are far more likely (and successful) to pick up your phone and make a call to the CG, Seatow, the marina just down the river, etc rather than hit the DSC emergency button. If the radio fails in the future because of age, you can replace it in a day with no significant rewiring or other steps.
Continuity won't tell you anything about the condition of the coax. I'd just replace the coax entirely if it is old. On a C22, you can get away with using RG58, which is thin, flexible, and easy to run/install. If you aren't confident in your ability to install the connectors on the end, it usually isn't hard to find someone who is. You can buy the coax with a connector installed on one end, which will be the most important end to get right the first time.
Mark