Hi,
Well, there is no contact us form in HikaShop for carts.
Why not create a payment method "contact us" based on the "collect on delivery" plugin already available and use its "shipping methods" setting to restrict it to the "contact us" shipping method you already have ?
Then, you can customize the text displayed by that payment method at the end of the checkout and configure it to set the order in a specific "contact" order status you would have first configured in the System>Order statuses menu.
And you could configure a custom order status notification email for the "contact" order status via the "per status override" button via the menu System>Emails so that you can have an email seen as a contact request email instead of a normal order notification.