I think if the live is on the fuse side, then leave it as it is, no matter how it's marked. There's been a lot of cases in Chinese design with the fuse on the neutral, and they've maybe later swapped the connections. The reality is it doesn't matter hugely, many pieces of equipment run off ac, which swings positive AND negative in respect to earth, and many have dual rails inside once rectified and smoothed which are +ve or -ve with respect to gnd.
It's just because we reference things to ground that we think it matters, what really matters is the potential difference. At high voltages, your body wont care if its touching +240V or -240V, it just knows that there's a potential difference causing current flow through you that will hurt and possibly kill. We reference everything to ground, because invariably we are standing on it when we touch something electrical, and we want to know if it'll let current flow through us.
It's why some of the cheap chargers can be so dangerous. A lot of times, the output isn't referenced to earth, and even through the two contacts inside might only have 5V difference (the potential difference), they may be sitting at 100V and 105V when measured between each contact and ground. So you can measure a small difference between two points in a circuit, but that does not mean it has a small voltage compared to ground, and isn't dangerous.
As always, when working with equipment with live mains, ALWAYS treat EVERY part of the circuit as if it is live, and could kill you. It'll keep you safe. It's also why isolation transformers are recommended when working on this stuff. It can stop you getting a full on zap. (unless you still go across contacts of both sides of the transformer.)