you could try using pliers to wind wire around a pencil. It has to be thick enough to hold its shape.
You can by ready cut mail on various arms and armour sites too.
My own way, aeons ago, didn’t involve riveting but DID involve pliers and hammers and small anvils, plus fairly close supervision (about one adult to every three or four kids). They’d be better off making coats-of-plates, or scale armour… round-nose scissors, card, and paper fasteners… easy!
As one of our workshops is making mail - the real way with wire rings and pliers but without the rivets - I have to say that your request did seem to be a contradiction in terms. Realistic, riveted mail with pipecleaners! However I register that your need is really for a simple, lightly supervised art activity so I think I can suggest a solution.
Garden centres sell small, lightweight, keyring style rings which I believe are actually used to help stake plants to small sticks. If the packs are too small for your requirements, you could always go straight to the manufacturer - they might be intrigued enough to help you out! However they are light enough that they could be linked together in fours with minimal risk to children's fingers and would end up with a rather more realistic effect than non-metal options.
The special effects people who did all the mail for The Lord of the Rings films wove together and then heat riveted over 2 million plastic rings - sliced from small gauge pipe I believe - so all things are possible!
I'm a modelmaker, a metalworker, a science show presenter and a designer and maker of hands-on interactive exhibits, and I can't think of an easy or cheap way of making realistic looking riveted chain mail - the truth is that it was never easy or cheap to make, for very good reasons. Put simply the links were individually riveted to stop them bursting open under the impact of things like spear points and arrows. Links that are simply closed together (like the modern chain mail used in protective gauntlets for butchers) stand up to chopping blows, as from a swung sword or an axe, quite well. If you shoot arrows at this stuff, or poke it with spears then the links will open up and let the point of the weapon through to the discomfiture of the wearer. So people who expected they were going to have arrows shot at them, or be poked with spears, and who had the cash were willing to pay the extra to have chain mail made from riveted links in the interests of survival. If you change the focus of your workshop from being a making things activity to being an investigation into the properties of chain mail activity you will, I think, get something rather better - and something which will link into CDT as well as history. Actually talking about the work chain mail had to do, and doing some demonstrations with a sharp axe, some arrows and a couple of bits of chain mail will get a class really, er, riveted. This activity will also allow people to start imagining the full horrors of a medeival battlefield