For something like a soup, it really doesn't matter how you cook it. Easiest would be to simply boil it in a flavored broth, but tastiest would be to grill it
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Maybe you could boil the chicken and then shred it with a fork? I do that with pork roast.
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I would slow cook it (think crockpot) in some chicken broth for flavor. Then it would be nice and tender, and shredable.
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When I need shredded chicken, I boil chicken breasts in seasoned water or chicken broth until they're ready to fall apart. Then I drain them, reserving the liquid, and set them aside to cool. By the time they're cooled off the chicken usually shreds really easy with a fork.

I took a look at the recipe you're using and it sounds delicious! I added it to my own All Recipes Recipe Box. Thanks!
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You can boil it, but you need to be careful, as boiling it can actually dry it out--that's why when chicken to a soup recipe you add the meat at the end.

The crock pot works well if you have time. DO NOT add liquid--to avoid the drying out problems that arise with boiling. DO leave the skin on, and place the whole chicken , or pieces, in the pot. Sprinkle with seasoning, cover and forget until dinner time.

If you're in a hurry, microwaving can work well. Wrap the chicken in plastic wrap, or place in a covered container, and microwave according to your oven's directions--different ovens will take different amount of time.

After cooking the chicken , let it cool, then pull it apart with your fingers to shred it.

Roasting or grilling would be fine as well--but a moist heat method will make it more "shreddable".

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