If the goal truly is privacy, and that's why you're adding cryptocurrency options, then adding a middleman like "proxysto.re" or any other, then you're not giving users the privacy you say you want to give. You really need to handle that on your end, if that's something you want to offer for the purpose of privacy.

Take a look at how Mullvad implemented it, which I guess is where you got the "cash in a letter" method from, they also handle cryptocurrencies by themselves for exactly this reason, there is no way for you to actually be able to fulfill the privacy promise otherwise.