My laptop battery started expanding to new territories (the outside, really), and given that it is no longer under warranty, I ordered a new one online.
But for the last week or two, I've been working on my laptop without the battery, and in the process I learned something useful.
If I close the laptop lid, and wait for the light to start glowing, I can then unplug the power cord, move to a new location and plug back it again.
The Macbook will use the hibernation feature so I can keep all my state even without any power.
Much better than the shutdown/startup process I was using until I accidently noticed this.