Hello,
I have a solution to suggest, follow me step by step :
1. Shipping method :
Create a Shipping method with as name something like : "define shipping method later" and of course, don't set fee or any cost.
2. Payment method :
Use the "HikaShop collect on delivery payment" plugin, and give him a name like "Ask for a quote" or "give me an offer"
AND add a restriction to your previous Shipping method.
Another, point that can be useful, is to define the Order status option that allow you to define (if required) a specific order status just for this "ask for quote or offer" order.
Hope this idea can help you to achieved what you need.
Regards