Saw tooth / tyre width

I probably want to buy new rims + tires for my golf. But I’m not sure about the size. At the moment there are 225 Michelin on 17″ on it. And even with the Michelin a sawtooth has formed again. According to the workshop you could not do much and otherwise everything would be ok with the car. But the rolling noise is especially loud, roaring and annoying in the village. Since the look of the rims is not so important to me anymore, I think about buying smaller ones. Therefore the question, o b there is also the danger of SZ formation, e.g. at 195 with Michelin? Or does the width of the tires have nothing to do with it?