Our logo consists of two shapes, for each one I'll use a different color (much like in the website header). I'll add the white one first.

Now, we need to fake the embellishing. To do that, we'll zoom in the document and create a new layer over the logo shape. I'll choose white and light gray for the colors here, but depending on what you want to embellish, you should pick others. For example, if your logo/design is red, pick a lighter red and a darker red, than the one used in your design. Using the pencil tool, alternate between your primary and secondary color (you can do this quickly by hitting the "x" key on your keyboard) and follow the "outlines" of your shape.

I first did the straight sides, and then copied and rotated to follow the other angles. Depending on the complexity of your shape, this may take a while.

Once you've done all the angles, group these layers (with the alternating colors) and set the opacity of the group between 30% and 50%. I used 44% in this case.

Now repeat the same steps with the other part of the shape (if you have it). Either way, congratulations, you just made your first plushie with a custom embellished logo.