I am not an electronics engineer, however here are a few things I noticed.
At 0:33 in the video you get a brief glimpse of the label on the unit, which reads “AC110V 12VA 50–60Hz”. That is the input voltage the unit is rated for. Strictly speaking, even 110V in the US would be out of spec and nothing is guaranteed here, but that might still be within the tolerance margin. However, 230V is more than twice that voltage.
At 0:54 you can see the entire PCB. The labeling in the top-right corner of the PCB reads “2.5A 125V 5A 125V”. So there are components on the PCB which are designed for 125V, but not for 230V.
Moerover, there is a large transformer in the center of the original power supply (same in the UK knockoff unit he is re-shelling), which appears to do the voltage conversion. Transformer-based power supplies designed to work with both 110V and 230V typically have a voltage selector switch accessible from the outside – the absence of one indicates the device will only operate correctly within a narrow voltage range – 10% more or less may still be OK, but more than 100% is not. Doubling the voltage you feed into the primary side of a transformer will also double the output voltage on the secondary side. Unless there is some more circuitry behind the transformer that further converts the voltage down, you will be running your N64 on twice the voltage it was designed for, with a high risk of frying it. If there is some further circuitry which converts the voltage from the transformer further down, that circuitry needs to be able to handle more than twice the input voltage it would get at 100V – else you will fry the regulating circuitry of your power supply (with possible collateral damage to the N64). Lastly, the transformer needs to be able to handle a doubling of the input voltage – else it might overheat.
And finally, why would the guy in the video go through all the hassle of gutting a 100V power supply and replacing the circuitry with that of a 240V one, when he could simply attach a UK mains plug to the Japanese unit?
While I have seen power supplies that work outside their intended mains voltage (an early 2000s cell phone charger rated for 220–240V, which worked fine on 110V – the other way round is less dangerous), this power supply does not seem to be one of them.
There’s a high risk of frying the power supply, the N64, or both, by running it on 230V. If you can’t find a replacement PSU designed for 230V, your best bet is to get a step-down converter, which will convert 230V mains voltage into the 110V your PSU was built for.