re: "I got a slight tingle" - that's usually a mA or two - which you should expect between hot and neutral with a high resistance, such as dry skin, and small surface area. Hot and neutral are the two sides of the power circuit.
The issue, though, is hot or neutral to the green wire, which is the chassis ground. If there are no 'leaks' and there is no neutral to ground bonding, neither hot nor neutral should complete a circuit through the chassis ground via the green wire. All you will see is a coupled voltage which is a high impedance circuit and can only provide microamps current.
The code, I believe, has a threshold of about 5 kw for gensets. This is where it starts to consider potential coupled circuits sufficient to possibly create a low enough impedance to allow a dangerous current.
For small gensets, it is generally safer to have the two power wires isolated from the chassis ground. Which of the two 'hot' wires is considered hot and which is neutral is mostly just a matter of how the plug is wired.
Gensets like the Honda 2k, and all modern gensets if I understand right, must have GFI circuitry. That will trip if there is any imbalance in current between the two power circuit wires.
It is also never a good idea to mess around with live hot wires!