I see two options:
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It’s possible to modify your cart page to make it a kind of contact form. Instead of checking out, your visitors will submit this contact form and you will receive e-mail with this data;
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Or, you can make your products free and uncheck “this product requires shipping”. Then you’d need to modify theme language to replace “Add to cart”, “Checkout” etc button labels. Your visitors will add products to cart, and proceed to checkout. This will require no shipping address and no payment details from them. Your will receive an order (which is in fact an enquiry) and a notification e-mail. This will require no coding, just editing theme language.