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It looks like you're going to need some sort of washer with a square hole to accommodate the portion of the square tang sticking up above the handle.
I'm not aware of any commonly available square-holed washers of any thickness*. I guess, in your situation, I'd measure the width of the square portion, select a regular cut washer whose inner diameter matched that dimension, and file the hole square with a pillar (square-section) or triangular (maybe easier to come by) file. Make yourself a little template from something suitably stiff and thin, so you can mark out the square. Take a marker pen (the sort of thing you use to letter on posters) and rub it all over, then align the template to the hole on the washer, and use a sharp awl to scribe a bright line, so you can see what to file to (you know those otherwise useless little awls that come in combination squares, stuck in at the tail of the combo head near the level vial? Perfect).
You'll probably need to stack up more than one washer; you want the final stack to be just taller than the exposed square. You might be able to cheat by measuring the corner-to-corner dimension of the square, and stack up washers that fit that dimension, finishing with your square-holed washer, so you have to file just one. But you do want a washer that fits the square, so the nut has something to bear on.
*You can get thin washers with tangs on them, used to make a square hole for a carriage bolt head when the wood's too soft to hole the head; but you'd have to stack up a whole bunch of them to make it work.