Ok, let me try to explain…
First of all; there are no exact limits on how much current a cable can handle. If you put too much current through a cable, what happens is that it acts like a resistor; it gets warm and you loose energy and voltage that you could be using to power your LEDs. If you really go overboard, the heat will become a problem, things will melt and/or catch fire.
However, the wire itself will be fine. A silicone-wrapped wire will happily keep conducting while the rest of the saber melts around it. Obviously that’s not what you want, but the point here is that the limits aren’t limits, they are guidelines that keeps your wires cool and efficient.
The same is basically true for switches. In addition to all of this, switches are rated for a specific number of cycles, at max current and max voltage. Switches rated for 3A@250 volts has to be prepared for the fact that while the switch is turning on, there is a short period of time where the switch is not fully engaged, and during that time, the full 3A will go through a much smaller contact area than when the switch is fully on. Also, 250 volts can cause small amounts of arcing (in the micrometer range) . Both of these things can pit and scar the contact surfaces of the switch. A switch that is rated for 10k cycles with 3A@250 volts promises that this pitting/scaring isn’t going to be a problem until at least 10k operations.
Sabers are much nicer on the switches though.
We very rarely operate the switch while the blade is on, which means that the current going through the switch is usually quite low when we turn it on/off. Also, we only use 3.7v, so arcing is basically not a problem. This means that our surfaces stay pristine much longer, which keeps the resistance of the switch low for a much longer time. So how much current can we put through the switch? Well, there is no great way to tell from the data sheet, but we can measure the resistance and estimate. I have not measured my switches, so I can’t say exactly what the limit is, but it is almost certainly much higher than 3A. Again, there isn’t a limit, we just don’t want the switch to become warm.
Generally, it needs much less than that.
The board peaks at around 4A, but the average usage is much lower, below 1A.