So, the issue here is power dissipation in the power cord, and voltage drop in the conductors causing issues for the electronics. Let's put a little perspective on this.

A 16 AWG copper conductor is about 0.0134 ohms / meter. The info I had handy was metric... or Real men use metric! :-)

A 18 AWG copper conductor is about 0.0214 ohms / meter.

Since an entire circuit makes twice the voltage drop (power cord is hot and neutral, gnd should technically not carry anything), we would double the numbers above for ohms / length of cord.

The above works out to the 16AWG being 0.0268 ohm/m
and the 18 AWG being 0.0428 ohm/m

This means the impedance of the 18AWG is 0.016 ohm/m more.

So, we can calculate the length of 18AWG cord that would present the same impedance as the factory supplied 16AWG cord.

That length would be the difference in impedance divided by the OEM cord impedance. For this case that works out to 0.016 ohm/m divided by 0.0268 ohm/m, or 59.7%.

So, as long as you replace the 16AWG cord, with a 18AWG cord that is less than 59.7% of the length of the OEM cord, you should be fine. That works out to 2.95', or for practical purposes 3'.

Now, in reality, the manufacturer didn't need every single bit of performance in that 18AWG cord. They likely spec'd it because it handled the required current, and was approved by the regulatory agencies. Many times issues such as, stocking the highest current cord increases our volumes, driving the price down, due to buying more of a given item, and only having to track one item in stock. Even if the cord impedance were the same, the voltage loss would be minimal, and certainly within the range of the tolerances from the power company.

So, this EE says, don't sweat it! You're not going to have any problems.

If you're really worried, go get one of the audiophile power cords with the ladder linked dielectric, and quantum spin matched electron guides. They'll only cost you a couple hundred dollars, and your sound stage will suddenly sound more open! LOL