there are several manufacturers of memory products that include an inexpensive MAC address chip in the product line. This will give you an 48 bit globally unique ID. I don't want to mention names/products since that may be against forum rules.
some come as small as TO-92 and SOT-223 with differing interfaces from 1-Wire, SCIO, I2C, SPI.
pricing, in modest quantities, can be as low as 30 cents US.
google "MAC address memory chip" if you want more info.
i've used several in past products that did not have an ethernet controller. with some ethernet controller capable MCUs they come along in the product so i haven't used them in several years.