The short answer is no. There is no product completely free of chemicals that will permanently straighten highly textured hair. The reason that a traditional relaxer is still around is because there's no suitable replacement if you want to straighten tresses without reversion at the first sign of moisture.
Now that that's out of the way, what about products like the Coconut Cream Natural Relaxer or a Wash and Wear Relaxer? When dealing with products like this, the word "relaxer" can confuse many people because what do you think of when you think of a relaxer? If you have any experience with the chemical process, you know that it permanently straightens the kinks and curls out of highly textured hair. The final effects depend on the original natural texture and how long you leave the relaxer on.
Products claiming to be natural relaxers are often little more than highly-moisturizing deep conditioners. Once applied to the hair, they can make the curls seem more relaxed simply because thirsty tresses respond positively to moisture. Weighing your mane down with large amounts of oil and/or fat will cause it to look differently, but it's not actually relaxed in any permanent form. In addition, many supposedly natural products require heat-styling to fully straighten the hair. Upon shampooing, the texture will likely revert back to its previous state.
If you want bone straight hair or hair that doesn't require a great deal of heat to straighten, you'll have to rely on the traditional lye or no-lye relaxer for now. If you do want to take the plunge and try a natural relaxer, be sure and read the ingredients list thoroughly, if you can even find it. In many cases, these products aren't chemical-free, which is contrary to its "natural" label.