You are like an electrical genious, lol. I'm useless when it comes to electronics, and if I had to beeak it down into components and wire sizes and load ranges I'd have a meltdown, I honestly think my brain would overheat :/ But you are like an Electricians text book, lol.Use 16 ga or larger (smaller number is larger gauge) to be safe. Nothing in a computer would be appropriate other than the power cord or wires directly off the power supply that feed drives or the motherboard. The smaller wires are useless for carrying AC current.
16 gauge is good to 3.7A, or 444 watts total load. This is more than you will need for a small cabinet incubator for heating element and fan and even a turner.
If you are building a small desktop incubator, you can go with 18 gauge, and lamp cord will be fine. You can also salvage this from a cheap 2 wire extension cord. This is rated to 2.3A, or 276 watts total load.
Never load up to the maximum load or you will risk a fire.