Sure, you can change your battery to keep things running...
Don't forget to recharge your discharged battery as soon as possible, as a depleted battery begins to 'sulfate' and the longer you let it sit, the worse it becomes - recharging returns most of the 'sulfate' back into the electrolyte solution if done in a timely manner...
I use 50 amp connectors to hook
12 volt stuff (air compressor, water pump, etc) to one of my batteries...
QuickCable: Product Details
It would be an easier way to 'change out' your battery as you described - get several 50 amp connectors (they 'mate' with themselves - if of the same color - usually gray) and mount a pair on your existing battery between the trailer and the battery terminals with enough cable length to make it convenient - then mount another connector on the spare battery so you can unhook the trailer battery and hook your 2nd battery into the trailer's connector...
You could then mount another connector onto your boat's battery cables to make it easier to hook up the 2nd battery...just a thought...
I've even got one of the 50 amp connectors with wires connected into a 'female'
12 volt socket, for any number of applications I might need...
Ray