It says to use 10 AWG because it assumes you want to actually pull 30-50A through it.
Since you're only expecting to pull 12A for this (the max that travel cord will actually allow) and it doesn't need to be long, 14AWG would be fine for up to 15A. No problem using 12AWG but I can't imagine 10AWG would be of any benefit, unless you want to run this extension all the way across your house AND try to pull 20A+ with some other device.
It's unlikely that it will have some sort of problem clamping onto smaller wire - the upper size limit is usually the hard cut-off. And if for some reason it really can't clamp the smaller diameter, you can strip a bit extra and double it back to thicken things up. Practically certain you won't need to do that though.
If you don't expect to use the wire for anything else, I'd suggest hitting whatever Home Depot like store is around and buy it by the foot. They will have it on reels and you can take whatever length you need instead of getting a larger roll. Whatever 14/2 + 16AWG ground or 12/2 + 14AWG ground they have. If you want to actually run it 25 feet, then you certainly could just use this https://www.amazon.com/Southwire-288282 ... B000BPG1ZC
. But if it's going to be a stub length, I'd personally grab a cut of 14/2+Ground by the foot.
And if you want to get stuff "faster" you can probably get both these plug ends there too, though I can't speak to the price.