This is a question so many ecommerce businesses are grappling with – especially those who won’t be able to pay their staff if they don’t continue selling.
It’s not clear whether couriers are going to be allowed to continue picking up and delivering non-essential items. In one business I work with, we’re currently taking the view that if we can pick and pack the orders within the isolation bubble (we have a family business, where the people doing the picking and packing are self-isolating together anyway), and the couriers are willing to do a contactless pickup, we should keep going to try to keep paying our staff.
I think there’s also potential reputation damage if you do try to stay open. For goodness sake don’t try to make the case that you’re an essential business if you’re not! The public is not being tolerant of people trying to find loopholes.