Rebeccca, I guess you mean corn stalks? not cork? I think you should use the stalks as
compost, at the very least. Composting is one of those processes that can break down bad stuff and make it harmless. Look up the term Bioremediation. That's when a natural situation can break down dangerous chemicals, and compost is one of those. But in order to speed up the composting process it would go faster if you chopped them up into small pieces, like chunks, layered with manure and grass, leaves, etc. Turn if often enough to keep the pile hot.
GMO doesn't matter unless there are seeds involved. Unless there are ears on there still that have seeds, then it's just carbon that may or may not have pesticide residue. Probably not enough to worry about if it's been dead for a while and sat through a lot of rain. If there are still some old ears on the stalks with seeds, I'd take those off and get them off the property, or put them in a metal garbage can sprayed flat black, with a metal lid and fry them to death in the sun for a year or so.
I don't know what kind of grey water system you intend to use. Mine uses live plants, not dead plant material. So you are going to just run grey water over a compost pile or something? I don't think the cold water would allow the pile to get hot and stay hot, which is what breaks down chemicals. But I doubt there's enough pesticide residue on there to worry about.
As far as mulch, I guess it depends on whether you want absolutely no chemical residue at all, or you think the compost under the mulch will handle whatever small runoff there is. If you are in doubt, mulch large perennials, like fruit trees or landscape plants. Not annual vegetables like tomatoes, lettuce, greens that are approx. 90% water.
I think using residue from unfortunate farming practices at least gets some good out of it

Mediterranean climate, hugel trenches, fabulous clay soil high in nutrients, self-watering containers with hugel layers, keyhole composting with low hugel raised beds, thick Back to Eden Wood chips mulch (distinguished from Bark chips), using as many native plants as possible....all drought tolerant.