Ah so what your saying is, the AC adaptor runs straight from a plug and converts there and then and doesn't have a box half way across the lead?
Most adapters these days you see have a box which then converts it, and so it isn't done on the plug itself.
I'd try and get one thats rated properly for your laptop to tell the truth. DC stands for Direct Current, while AC stands for Alternating current (What plug sockets use).
The DC connection must be transferring this AC to DC in mid flow. Batteries themselves use DC current, though I wouldn't use one not based on the laptop.
For instance, that 1V fluctuation on both might not even work it anyway, since it might need 20v to run, not 19. If you are worried, take out the battery and try and run it. The laptop might just refuse it.
You should be able to find a capable one somewhere
Didn't the new laptop come with a power lead? Or did it break?
Hope this helps