Search terms for serial number IC or memory dump without initialization?
Your idea is correct. The 1-wire products are widely used for that. However you can look for a serial number alike in various places, in you MCU for example:

If you have ethernet or bluetooth it will have a MAC which is globally unique;
Some MCUs have some kind of production marker (TI calls it 'silicon record'), so from the wafer id and coordinated you could compute a useful silicon number;
Some MCUs have an 'unclonable' facility which is actually a unique number which is factory assigned;
If everything else fail you could generate some kind of truly random bit sequence (something like 128) and save it in flash/eeprom; this is a kind of UUID too and it's useful as a serial number.

When above I said MCU you could look for the feature in FPGAs and even some peripheral chip.