I'm not sure what other option you have, besides going the route you describe based on the parameters you outlined. My two cents, it is better that you have the items on hand - but when people order online it is not unheard of that items don't ship right away or not on hand. I think what you need to do is think about the weakness of your strategy and how you can best offset that. For example, be prepared how you are going to explain it to the potential customer. Another issue, what happens if they return it. Does your supplier have a return policy - or you stuck back to a situation where you have inventory. Orders also get canceled, what happens if it occurs after you have placed your order. In some cases, I have clients that have the goods directly shipped to the customer - which can save time and costs. That might be something to consider, but maybe not if your supplier won't or you are concerned about the source becoming known.
I wouldn't let it stop you - just try to address it the best you can for now.