Ah so you are planning on buying clippers and doing it yourself? I just goggled those breeds, as we don't have them in Australia... The Navajo-Churro breed seems to have a more carpet type wool. I'm not sure of any differences in shearing the more carpet type wool as opposed to the super-fine wool we shear here. You would need clippers with a wide head, otherwise it will take you forever!
Just through a google search... Actual Shearing handpieces are very pricey... You could try horse/dog clippers. Not sure how they would cut through wool though.