Wire converter to which side of battery switch?

If the idea is to be able to run the rig on the converter with no battery, and that's the only converter, then by the battery

If you have the old converter still hooked up inside the rig, and the deck mount up by the batts, then you can have the switch on the battery to old converter pos wire where it is now, and no switch for the new converter at all.

That would let you run the rig on the old converter while the new converter charges the batteries with no load on them slowing down the recharge.