I've posted a couple of times about fixing up the old White 565 sewing machine I got from my Grandma. It has a thin cord with a small non-polarized plug, and does not have a main on/off switch. It still plugs in and runs perfectly.
The problem I wasn't expecting is that it creates electromagnetic interference (EMI). I found this out when I was using it at the same time my Dad was watching TV. It caused static on the TV. I was able to fix this by plugging the sewing machine into an isolation transformer. The isolation transformer eliminates the interference, plus it adds a main switch.
Another way I could try to fix this would be by adding a ferrite core. If it works, it would be much cheaper than having a dedicated isolation transformer for the sewing machine.