To take a snapshot of a window that is larger than the screen, you will need to enlarge the screen,
since a screenshot cannot contain pixels that have not been painted.
When using the Windows applet
Control Panel / Appearance and Personalization / Display / Make it easier to read,
only allows to increase the screen DPI, not to reduce it.
Nevertheless, there is a way to reduce the DPI which involves registry editing.
From the article Zane's Blog - LogPixels DPI hack :
Here's a handy tip for those netbook users out there in dire need of
more screen estate. You can force a DPI value of lower than 96 by
using the Windows registry.
To do so open regedit, navigate to
HKEY_CURRENT_CONFIG\Software\Fonts
, item LogPixels
and change the
decimal value from 96 to something lower such as 80. Then log out and
back in and you will see the changes.
I'm using a value of 80 on my netbook and it is about the most that I
will drop it while still keeping things (half) readable. You will
notice that it really hinders the readability of fonts as well as
having some strange bitmap scaling artifacts, but if you're like me
and can adjust to it then the extra screen space gained is well worth
it.
You can view a side by side comparison of the my desktop with
LogPixels at 80 and at 96 :

Before modifying the registry, export the Fonts branch as backup, and also create
a system restore point.
It might be a good idea to export the .reg file to the desktop when making these experiments,
so be able by a simple double-click to activate it and restore the original sizes.