From a culinary and food safety standpoint, cooking enoki mushrooms is essentially non-negotiable. While you might occasionally see older recipes or menus that use them raw as a garnish, food safety agencies such as the FDA and CDC strongly advise that enoki mushrooms should always be cooked thoroughly before eating.
The main issue is Listeria monocytogenes. Enoki mushrooms are cultivated in cool, moist environments where Listeria can easily multiply, and there have been multiple notable recalls and outbreaks tied to raw enokis. Rinsing or soaking them in water will not eliminate bacteria that have adhered to the surfaces or penetrated the delicate clusters. Heat is the only reliable way to destroy the pathogen.
From a texture and digestive perspective, cooking is also beneficial. Mushrooms have cell walls composed of chitin, which the human digestive tract cannot break down easily without heat breaking those fibers down first.
Your suggestion to flash them on the flat top grill with a bit of butter and soy sauce is a fantastic option. A quick sauté over medium-high heat for two to three minutes until they soften slightly and become aromatic will keep a pleasant tender-crisp bite while ensuring they are completely safe to enjoy.