Washing soda (sodium carbonate) will precipitate the copper as insoluble copper carbonate. But it will do much the same with the iron and any other metals in the mixture. This means you will have to add quite a lot (but washing soda is the cheapest chemical, really. Much cheaper and more effective than bicarbonate which is recommended by some). There will be quite a lot of fizzing, and froth, so the mixing should be in a bigger-than-needed container (made of plastic, I suggest).
Copper carbonate is a duck-egg blue solid, and ferrous carbonate green, while ferric carbonate is nearly black. So what you get as precipitate is going to vary in colour, but the main thing is that the solids are not soluble, and the remaining liquid (which will still include some Sodium Carbonate*) can go down the drain.
*you can tell the reaction has gone all the way by adding more sodium carbonate, and if it does not fizz at all, you are there.
The solid stuff is relatively harmless, so dry it and drop it in the bin. All the chemicals in it are found in nature, and some are used in jewellery, so if they are OK to hang round the neck of a queen, …
Cheers, Tim