You should put all your products without prices but turn on the option "Display add to cart button for free products" in the Display tab of the configuration of HikaShop and also change the word "Free" to something like "Budget estimation".
Then, users will add your products to the cart and finish the checkout. there should be no payment asked since the price would be 0.
Then, you will receive an email and you will be able to edit the order in the backend in order to set the prices and the payment method.
Once done, you can give the users a link to their orders listing where you will be able to display a "pay now" button for created orders which are not yet paid but turning on the option "Payment of orders not paid immediately" of the Checkout tab of the configuration.