I know another business that could easily make the transition to online: art galleries.
Sure, not all art is suitable to be bought online. Especially not 3D art like statues. Maybe not even paintings, where the structure of the paint on the canvas adds to the quality of the work. But in the case of graphic work (etchings, lithography, woodprints, photos), it is very well possible to take high-quality photographs of the work that allows the prospective buyer to evaluate the work before buying it. Shipping is fast and easy, because there are standard packages and rates for flat 'documents'.
If you have an online art gallery with focussed offerings, you could do brisk business. If you make sure your after-sales service is excellent, the experience of shopping at your site might be superior to shopping at a brick-and-mortar gallery.
Case in point: Japanese woodblock prints. We bought one at Hotei, in Leiden. We couldn't take the print with us right away, because it had to be framed first. I had to pay for the frame right away and then leave my contact details so they could send me an invoice for the print itself. We would then collect it later.
After about a week, I sent them an email asking after the invoice. I never received a reply, but a few days later we received the invoice on the (pretty!) Hotei letterhead. The invoice consisted of... two lines. I wonder why it took them so long.
We paid immediately (though internet banking) and we haven't heard anything from them since. We plan to collect the print this Saturday, but we don't even know whether it's been framed yet!
We also bought this print from Fuji Arts. I paid online through PayPal and received immediate confirmation. The next day, I received a mail from their shipping department asking whether it was OK to put the true value of the package on it, with regards to customs. I asked them to do something... creative and promptly received a reply confirming that they sent it out according to my wishes.
Three days later, the FedEx guy rang our doorbell. All in all, it took less than a week, and it all cost less than the print we bought in person at Hotei.
I know where my next print purchase (if any) is going to be made.