A unique order number key instead of a letter of guarantee.
You do know the purpose of a Letter of Guarantee, right? It's so the user has hard evidence in case you don't deliver. A "unique number" proves nothing. I can think of only one reason for not providing one: it helps cover up a potential scam. If you have good intentions, why risk people thinking this way?
You don't need to download anything, just copy it and save it
You can do that with a Letter of Guarantee too

Hello, LoyceV! The order number key function is identical to the letter of guarantee function - in case of problems or disputes, this will be your personal and only proof that a certain transaction in the mixer belongs to you. Of course, there is no scam here. In addition, if problems or disputes arise, the letter of guarantee will testify and be proof that your ownership right (in this case, bitcoins) was sent to the service and at the moment of misunderstanding is in it, and not with you or anywhere else.
BUT IT DOES NOT GUARANTEE a REFUND of these funds, as you yourself mentioned, if the operator turns out to be a fraud and decides to appropriate your coins.
To sum up: the letter of guarantee guarantees the evidence base of the actual location of your funds in the service, but not their return back to you.There are no additional risks for customers due to the order number key, once again - there is not and cannot be. Perhaps you just don't understand how this element functions. Well, dear LoyсeV, we will tell and describe both to you and to all other outside observers how the order number key works in the system, because we are here for this:
After filling out the mixing order form and confirming it, a mixing order is created. At this moment, the Order Number Key is automatically generated, assigned and attached to it (the order) to all other data you have entered, respectively. In other words, order number key combines and becomes one with all the information about your order, and, accordingly, it is broadcast on our servers together with it.
Order number key is unique.