The notes of a whole tone scale form a checkerboard pattern on the fretboard. Every other note is a member of the scale, and the frets that these notes fall on invert each time you go up or down a string.
One way to play the notes of a whole tone scale is to keep your hand in place and play all the notes accessible without shifting. This creates one of two patterns, depicted in the fretboard diagram above.
In one, your first and third fingers can play notes on the second and fourth strings, while your second and fourth fingers can play notes on the first and third strings. In the other, the reverse is true.
The downside of this method is that you can't actually reach every note of the scale. To do that, you'll have to shift at some point.