Human skin has a pretty high electrical resistance at low voltage (you can measure it with an ohmmeter, just grab the probes). If you stick your finger on low voltage like below 24V you won't feel anything. Some current will pass in your finger but it will be microamps. Last time I punctured a finger with the pointy end of a wire that had about 12V on it, I did feel a small shock, because that bypassed the skin resistance.
Wet/sweaty skin has lower resistance, and mucous membranes much lower. Back in the day we used to check if a 4.5V battery was still good by licking the terminals, I don't think anyone died from that. If you try it with a 9V battery though, you won't try it again.
But, just because current is flowing in wires doesn't mean it will also flow into you.
Above a certain voltage, skin "insulation" breaks down, then its resistance becomes low enough to let a dangerous current flow. You could think "ohm's law", so touching a wire with 230V would cause about 10x more current in your finger than at 24V, but this is not true. At 24V the skin is a good insulator, but not at 240V. So at 230V the resistance is much lower, current increases dramatically, and you get zapped. That's when you absolutely have to take precautions.
But if you only use low voltage, no problem. Safety is more about not getting burned with the soldering iron, not breathing the solder fumes, and not getting bits of exploding MOSFET in your eye.
If you solder or probe on powered circuits, you can cause a short and destroy the circuit, then you drop the soldering iron on your finger.
And if you solder or probe on a powered circuit using LiPo batteries, what you should be worried about is fire...