I have no question about the efficacy of Nirvana-Shop when ordering via credit card. The thing with sending cash is that it would take a lot longer, as others mentioned up to several weeks. When you send your cash you're basically relinquishing it to fate. It could be lost in the mail, but a much larger worry is that whoever opens it will simply take the cash and destroy your order form. And Nirvana might not even be to blame, it seems like cash is being sent directly to the payment processor (Themis Pay). Sure you could go with registered mail, but all that would prove is if the letter was ever delivered; not that any full payment was assuredly received. Perhaps the risk is why there are no shipping charges as someone already suggested.
Maybe you could make a note with your e-mail and they would send you details about the progress of your order, but then there goes your lack of a digital trail... albeit less of a trail than a credit card linked to your name and address.