question regarding customer shipping address

I have a question that I cannot seem to find an answer to in the previous threads.

I have a separate online business, and would like to include some of my prints for sale to my customers, but not through my SM website.

I am wondering if it is possible, when they make an order, can I purchase the prints myself, thru my SM site, and have them shipped to my customer in order to keep the shipping costs and times to a minimum for both them and myself. Or do I have to have them shipped to me since I am the one paying for them thru my SM site?

If there were any problems with the customer not being satisfied, I would handle the problem on my end, and go back to SM myself.

Thanks!