First off I would recommend that you do this transaction privately via email. Then when you show up to pick up the animals, I will require two sets of fingerprints on an official FBI form, three letters of recommendation (none of which can be from any relative of yours), 12 forms of ID with photos taken within the last 30 minutes, and the keys to your car. Oh yes, and I will give you a secret dance step that you will HAVE to perform in front of my tables so I will know it is really you.
Seriously, this has never been a problem before. Simply because I don't broadcast my transactions publicly. The chances of someone knowing exactly what someone has ordered and all of the details are really pretty slim.
When someone shows up to pick up an animal held with a deposit, I always give them the option to pick out another one (if I have more) if that would be more in line with what they want. I try to hold back the prettiest one, but that is pretty subjective, and I would not require you to agree with my decision.
Sound fair enough?