The keyboards for the Surface (and surface-alike) tablets vary, but none of them really work well for lap use.

"Too big" is entirely subjective; for my own taste, the slight size differences among this class are pretty much an irrelevancy (and indeed, going much smaller than the Dell produces a keyboard too small for my comfort.)

You might also look at the Macbook Air 11", although the width is at the high end of the range.
Height: 0.11-0.68 inch (0.3-1.7 cm)
Width: 11.8 inches (30 cm)
Depth: 7.56 inches (19.2 cm)

Any recommendation of the Macbook/Macbook Air depends on running the MacOS one them.

Onen machine which will not feel that much faster than the Vaio X, but which is incredibly inexpensive is the HP Stream 11. It's basically the Windows equivalent of a Chromebook. 11.8 x 8.1 x 0.71 in, 2.57lb, but $199 MSRP.

The pricessor isn't awful, but the the eMMC storage is cr*ptastically slow. There seem to be a whole bunch of other similar 11.6" ~$200ish low end Windows laptops