That is not such a simple question to answer.
The specs you mention are dancing around the question but not actually nailing it. Plus, they are incomplete, so we can't actually reference "950 watts per channel" into something meaningful without more descriptors.
Just by way of example, if that's 950 watts into 4 ohms with one channel driven, it's one thing; if it's 950 watts into 4 ohms at 20~20,000 Hz, both channels driven, at x% THD, that's another (the latter spec will mean it probably draws more current from the AC supply). If it has a conventional power supply, it may be only 55% efficient; if it has a switching supply, it may be 90%+ efficient. The latter will require less current draw from the AC supply. And so on. (I can tell you the Sansui definitely has a conventional supply, and, without looking at the specs online, it sounds like the Yamaha has a switching supply).
Actually, I did give the specs with everything you mention except "both channels driven". The Yamaha spec say in stereo mode, so I would presume that means both channels driven.
Yamaha literature states:
EEEngine (Energy Efficient Engine) Technology makes more efficient use of AC power by reducing power consumption and heat generation without sacrificing output power or sound quality. When power requirements are low, the system uses a highly efficient current buffer to transparently switch input power on and off as needed. As power requirements increase, an independently responding auxiliary power line supplies additional power as required. Output isn't compromised because the auxiliary power line is driven by the power supply voltage which maintains maximum output to the speaker load.
I think you are right - that seems like a gussied-up way of saying it has a switching supply.
The important one is the current draw in Watts (voltage is also an issue, but it's 120V in the US, mostly, for audio gear).
That must be listed on the unit near the AC cord. I think (don't quote me, but you could look it up) that if the current draw is somewhere around 350 watts or less it's OK with 18 GA. You should be able to read that by examining the unit; either embossed or on a sticker. It's supposed to be on every thing that plugs into a wall outlet.
You also want to see a certification lab mark; UL (an insurance industry certification; Underwriter's Laboratories) and CSA (a Government safety testing lab, Canada Standards Association) are good and are considered equivalent. There's more, but basically you don't need to worry about it much if one or more of those marks are present and you use the gear in the US or Canada.
Be aware that it's hardly unheard of for cheap imported goods to counterfeit the marks. More common with lamps and cheap consumer goods, but not unheard of with audio gear. Buy from trusted manufacturers if there is any doubt. It's also possible, but not exactly easy, to cross reference the number to see if that matches the unit, or if it exists at all.
Although I don't know of many actual cases, it's possible that if an amp burns your house down, and it isn't certified by one of those two, they can deny your insurance claim. For the whole house. Just so you know. That's where we extend the "buy from trusted manufacturers" to "get insurance from a decent company" that isn't bent on denying claims at all costs, if only because you don't want to have to settle for less or go to court.
Also, the unit will be certified based on the regulations in existence when it was made. It may not pass today's muster. Having said that, if it passed at some point in the past, it's still OK to use it today, assuming it's in good condition.
My Yamaha amp seems to be running under the radar. It has no markings! The cord is marked UL and CSA, but I'm not sure if that applies to the generic cord or applies to the specific amplifier. Could the markings be inside? I wonder if pro-amps are somehow different? Yamaha is a pretty established player not to be meeting industry norms!
Oh, and How About Dem Saints! It's the first time in about a decade that a team I cheered for won. My rule is if my team doesn't make it, I cheer for the other conference.