if the new unit only has 1 live output terminal both your existing wires can be joined at the output terminal. u can get a piggy back female connector which has a male connector on it as well as being a female.
All u have to do is cut off the connector on the battery lead, crimp on the piggy back & push on the lights terminal, as it is an uninsulated terminal wrap it up with insulating tape or get a piece of heat shrink tubing and cover with that, job done for minimal disturbance/effort/time/etc.(i am assuming there are fuses already in these lines.)
I just fitted a new one to a van this week, it was one i'd not seen before, it was either a powerpack or powerpoint, 13.9 volt 10amp nominal output 12 amp max, seemed a decent unit.
As for running mains without a battery, now thats a sore point with fitters, me included.
If u have a battery on its like a reservoir it smooths out flow & keeps things nice and gentle, if u havent got one on, when u put 240 into the cvan its initial surge can and does send a spike throughout the system, which on occasion fouls up sensetive equipment, like trackers, or alarms & it wouldnt be the first time we've had to replace a power relay on a swift 645 that uses a key fob remote to switch the power on, simply because the handover lads are too lazy to connect a battery to it first.
Had to do one 2 weeks ago for that reason.