What is the substitute for pastry blender in cookie making?
No, the device called for, a pastry blender, is not what you have linked in either picture.

The first is a simple hand mixer with standard beaters.  The second is the paddle attachment for a stand mixer.

A pastry blender is used to cut butter into flour and looks something like this:


(Image from crate and barrel)

It is used to cut butter into flour, while leaving it in relatively large solid chunks.

If you don't have a pastry blender, alternatives include:


Using two knives, criss-crossed, to slowly cut the butter up with the flour mixture in a scissors-like motion
Pressing with the back of a fork
With skill and cold hands, you can even press the butter and flour together with your fingers, which is very old fashioned, but hard to describe in text

(All of these methods require butter cool enough to not blend into the flour, but warm enough to cut easily, about 65 F, 18.3 C.)
If you have one, cutting in butter is also very easily done in a food processor with the knife blade; in this case, you want cold butter.  It usually takes not very many pulses, so monitor the texture after each pulse or two once you have done four or five.
If you have a large holed grater, you can even grate frozen butter, and then simply toss it with the flour


This video from Dear Martini Kitchen has an excellent demonstration of the pastry blender method that clearly shows the desired texture, an inset which shows the two-knife technique, and at the end a brief food processor demo.