My dad's house was built in 1955 and all the electrical wiring had metal conduit around it. The backplate of the switch was also metal too.
So what he did was connect the ground wire to the metal backplate behind the switch to ground it.
Another option you can do... or should I say have an electrician do... is to pull all the two-wire electrical wiring out and replace it with three-wire cabling.
You would need an electrical wiring schematic available and go to your circuit breaker and then turn all the power to your house off. Then one pair of wiring at a time, remove it from the actual circuit breaker itself, have 3-wire cable firmly attached to the 2-wire cable you currently have (soldering them together and taping them is the best method. Then go to the wall socket or wall switch and disconnect the other side of that pair from the socket or switch and just slowly pull the 2-wire out with the 3-wire attached. Once the three wire comes out the other end, just cut the 2-wire to 3-wire soldered portion and reattach the wires to the socket or switch and ensure the ground wire on your circuit breaker is firmly attached to ground.
Depending on how large your home is, that might cost quite a bit but you could probably get an estimate and see whether it's worth it or not. It would upgrade the electrical status of your house which would give for a better appraisal value if you ever wanted to sell it.
Here's an article you might find interesting: Do Light Switches Need To Be Grounded? - LED & Lighting Info (ledlightinginfo.com)