Just one Rube Goldberg-style idea:
You could generate a table with a random set of numbers that is tied to a random period of time:
Time Period Interleaver
next 2 weeks: 442
following 8 days: 142
following 3 weeks: 580
and so on... this gives you an unlimited number of Interleavers, and doesn't let anyone know your rate of orders because your time periods could be on the order of days and your interleaver is doing a lot of low-tech "mashing" for you.
You can generate this table once, and simply ensure that all Interleavers are unique.
You can ensure you don't run out of Interleavers by simply adding more characters into the set, or start by defining longer Interleavers.
So you generate an order ID by getting a sequential number, and using today's Interleaver value, interleave its digits (hence, the name) in between each sequential number's digits. Guaranteed unique - guaranteed confusing.
Example:
Today I have a sequential number 1, so I will generate the order ID: 4412
The next order will be 4422
The next order will be 4432
The 10th order will be 41402
In two weeks my interleaver will change to 142,
The 200th order will be 210402
The 201th order will be 210412
Eight days later, my interleaver changes to 580:
The 292th order will be 259820
This will be completely confusing but completely deterministic. You can just remove every other digit starting at the 1's place. (except when your order id is only one digit longer than your interleaver)
I didn't say this was the best way - just a Friday idea.