Can I use a regular 2512 SMD Resistor (0.001 ohm) for HLW8012 IC shunt Resistor
Indeed you can, at Sonoff they also wanted to save a few cents so they did this:



Image from this site.

Note how the sense wires partly go under the shunt resistor.

Note that if the solder connection isn't good / reliable this can influence the total value of the shunt resistor + solder contacts. That issue is avoided when using a 4-terminal shunt resistor.

Note that at 1 milli ohm, it is easy to get a little extra resistance here and there.

As Andy aka comments: accuracy might be compromised.

Maybe that can (partly) be compensated for by a calibration.

It depends on what your priorities are (accuracy / calibration and cost).