It's pretty common to use saw bushes for blades with a larger bore than the shaft diameter that you've got. The problem lies in really cheap inaccurately made bushes (They're just punched out of a sheet like cheap washers) which can introduce a wobble to the blade if the bore of the bush is not exactly concentric to the bore of the blade which in turn causes vibration. The best you could get is a precision turned bush from an engineer which is absolutely dead-on and is a snug fit in the bore of the blade.
Another thing to keep in mind is that if your saw has cupped flanges with recesses larger than the size of the washer it can come loose and drop out of the saw plate, which has pretty nasty results:
Some people like to take a punch and pein a couple of dimples around the bore of the saw to hold the bush in but I don't not a huge fan of this as it may upset the tension in the saw plate and warp it, I think the fella in the video has a pretty good idea of putting fibre washers each side of the blade.