You can simply unsolder the clips/lug from the PCB - you cannot unsolder the lugs from the battery as they are welded on and you must break them off if you want to use a battery without the lugs fitted. If you buy the new battery from Jaycar it will have the lugs installed and you simply solder the new battery in. Make sure you don't overheat the PCB when unsoldering.
In the attached pix you can see the blob of solder under the PCB which holds the clip/lug to the board.
Just priced a new key head for a VY today from Mr. Minit. $109.95 including programming.
At this rate a new key will be worth more than the car by August 2017.