Hi,
You can create a custom field of the table "order" and of the type "advanced date picker" via the menu Display>Custom fields:
www.hikashop.com/support/documentation/4...shop-field-form.html
That way the customer will be able to select the date during the checkout and the information will be included in the order, and you have display options to display that information on the orders listing or not, the emails or not, the invoice or not, etc.
Please note that this requires HikaShop Business. If you have the Essential edition, you would have to upgrade it via the menu My account>My subscriptions on our website.