It's a given that any wires in cordage will be stranded. Being designed for a different kind of service is what makes cordage different from in-wall wiring, and why you should not use one for the other.
So it's a given that any plug whose primary use is cordage is designed to work with stranded wire. Here, you should follow the instructions and labeling on the plugs, because following those instructions are the basis for the testing and certification which the plug received from your NRTL. (Nationally Recognized Testing Laboratory) such as UL, CSA, TUV etc.
Not following the instructions is an "off-label use" (to put it kindly) and can result in an illegal install and non-payout of fire insurance.
Speaking of non-payout, you need to be careful what you are sticking on mains power, and in particular, built into walls. Random electronic components out of the Digi-Key catalog are unfit for use in mains power. Equipment made for use in mains wiring can get its cert/listing faster if it is built with listed components, that is all a component listing means, it does not mean you can use components directly.
So for instance "random relay" is not listed for use in mains, but an "RIB" unit containing that same relay can be used. (RIB ~= Relay In Box).
If your aim is smart appliance control, you may be better off using existing, listed/certified smart devices (i.e. Not Sonoff), and having your electronics communicate with them. Generally, the rules are greatly relaxed for homebrew equipment when it is entirely low voltage and fed by a listed/certified wall wart.