I do a lot of drop ship and so I have this problem too. There are a couple of ways you can get around this.
First, CPSIA only requires that your name and location (not a web address) be on the label. You can ADD a web address to that if you want, but it has to have your physical location. This adds a layer of Googling to anyone who wants to find you directly, and that's actually quite a barrier. Only the most determined would go to the trouble, when they already know they can go to your customer to get the goods. The downside of this is that maybe you were hoping to use the same labels for your retail stuff as for your wholesale stuff.
Second, there's the wholesale agreement that VulvaLoveLovely mentioned.
Third, the law says that the name and address of the "manufacturer OR private labeler" be on the label. You can set up your wholesale accounts who don't want to have your address on the goods as "private labelers" meaning that you make the goods in their name. You will, of course, need to ask them to pay more for the privilege. Your wholesale customers might also want to keep in mind that when they become a private labeler, they assume responsibility for the CPSIA testing. They will then decide how important their branding is to them. Either they'll pay what it takes to get them their own labels if their brand is that important to them, or they'll allow your labels to be used.
