What model of converter do you have? If it's the original equipment one, the tender might treat the batteries somewhat more gently. You should make sure the batteries are fully charged before using the tender, though; it doesn't have the guts to recharge the large batteries (or even smaller ones very well).
If using tender, converter should be off, which is easiest to do by disconnecting the shore power cord. It may be more convenient to turn the converter off with its breaker in the motorhome (or by unplugging it from its outlet or some other means), so that you can plug the tender into the RV electrical system.
If not using the tender, leaving the shore power cord connected or connecting it from time to time will help maintain battery charge.
What to do with the aux battery switch depends on what it actually does and how the RV is wired. If it's a typical house battery disconnect, you may need to leave it connected for the built-in converter to charge the battery. If it's to connect the house and chassis batteries together for starting purposes, it's best leave it disconnected. If it's simply to switch the radio from one battery to the other, I'm not sure it really matters much.
For winter storage, you can also charge the battery fully and disconnect the negative lead and just leave it alone.
If you have the original converter, I would be tempted to simply upgrade it to a modern multistage one rather than getting a tender. The PD 9200 series (deckmount) or equivalent 4600 series (mount into a power center chassis) are well regarded, though there are others that are also good.