After my original post on the subject, I did more searching on the net and eventually decided to purchase a pair of Sony MDR-ZX770BN headphones; these have received good reviews and are not too expensive. I could have bought a pair from an Israeli supplier at what appeared to be a slightly higher price than the British supplier from whom I bought, but once other factors such as shipping and customs charges were taken into account, it looks like I made a poor decision regarding the vendor.
As these are proper headphones made by a very reputable manufacturer, the packaging was extensive: not just a plastic bag, but a box which fits inside a box which fits inside another box! There are also legible instructions in about fifteen languages (although Hebrew does not appear to be one of those).
As seems to be the norm with such headphones, they receive their music via Bluetooth or via a cable. For the time being, I'll have to connect the headphones to my old (but good!) mp3 player via the cable; it might be possible to tape the player to the headphones. I have ordered a Bluetooth mp3 player which accepts a memory card, so I won't have the cable problem in the future. These are not the outcomes which I wanted but they are acceptable.
I used the accompanying USB cable (the same as my Kindle cable) to charge the headphones. A red light did come on to show that the headphones were charging; presumably it turned itself off when the battery was fully charged (I'm not sure about this). A press of a few seconds on the power button turns the headphones on; I think that a press on the 'nc' button turns the noise cancelling function on. I can't hear any difference at the moment but then I'm sitting in a quiet place.
The real test will be in two days' time when I travel to Karmiel. Will I hear extraneous noise? Will I hear my music at a reasonable level? All will soon be answered.