The simple answer is to do your homework and ask the right questions, which you're already doing. Cork is considered a more sustainable flooring alternative to wood since cork regenerates and can be ready for harvest again in less than ten years. In addition, the harvesting process does not kill the trees.
On manufacturers' websites, look for a description of the product you're considering and see if it mentions sustainable features such as low-VOC finishes and no-added-urea-formaldehyde plywood backing. Most companies that are going to the trouble of selling alternative products will do their best to get the word out. If the descriptions don't mention sustainable features, the products probably do not have them.
If you are skeptical about a company's claims, ask for the material safety data sheet (or MSDS) for the product. The MSDS is generally available to any installer. Most companies will have these available on their websites, and retailers must make them available. They can be dense with mostly irrelevant information, but they can be a great resource.
Finally, in response to your question about water-based polyurethanes and acrylics having VOCs: Yes, they almost always do before they are applied. For example, many water-based products contain glycol ether. It may sound bad, but these products are biodegradable, do not persist in the environment, and do not bio-accumulate. This is true of the commercial products applied at the factory as well as the types you would apply on your own. But more to the point, water-based finishes almost completely offgas before a prefinished product arrives on your doorstep, unlike other solvents and resins in traditional finishes.
The bottom line is that there are no magic products that are not harmful, only ones that are significantly better. Water-based products are definitely significantly better, both for the workers applying them and for the homeowner.