I want to re-wire an ac to dc power adapter for an ONT(Optical Network Terminal - AKA Fibre Box mounted on a wall) and replace the adapter with a standard DC plug. This is because I want to connect it to a UPS(uninterrupted Power Supply). How do I tell which one of the two wires is the live or positive wire in this picture?
You don't have a voltmeter. Do you have a potato?
With the power adapter unplugged from your electrical outlet, cut the wires, strip a little insulation from the ends, twist the wires into a point. Do not allow the bare wires to touch each other from this point on.
Cut the potato in half. Poke both wires into the cut face of the potato about 2 cm apart. Plug in the power adapter to the wall outlet. In a short time, the potato around one of the wires will turn green. That is the positive wire.
Unplug the adapter and clip off the ends of the wires so you have clean wire for soldering your new plug.
From personal experience: don't rely on the wire marking in regard to polarity.
I had once the boring task of shortening some power brick wires from a single batch.
I ended up swapping some bricks vs some jacks and - surprise! - about 20% of them failed to work.
Luckilly, the devices were tolerant for wrong polarity so I only lost ~2 hour of work.
Since then, I always use voltmeter.
About 70% of these are marked wire negative, but the other 30% are marked wire positive.
In North America the marked (striped or ribbed) wire is neutral (or negative, when it's actually DC). It also has a wider blade on the plug or connects to the outside of a barrel. The conductor sometimes has aluminum blended in with the copper.
I don't know South African standards, but I've never had a universal or international cord that was otherwise.