That’s an easy question to answer: Not dangerous at all.
But apparently the question gets asked a lot because the Wikitravel page on the Israel National Trail specifically states:
Carrying a weapon is completely unnecessary.
So, this hiker whom I saw in Jerusalem was a bit over-equipped with his stick and pistol.
I once hiked the Jesus Trail in the north of Israel, four days from Nazareth to Capernaum by the Sea of Galilee, and there was nothing dangerous at all. Actually, come to think of it, I should finally write and publish the complete account of this 4-day hike.
I assume that on the desert part of the Israel National Trail, lack of water and the sun can be dangerous, but oddly enough, that’s not what people have in mind when they ask “But isn’t Israel dangerous?” I would generally advise not to visit Israel in July and August because it’s too hot. And before setting off on a walk, get a few bottles of water and a cool hat.
Now, this got me dreaming of walking the Israel National Trail. It’s only 1,000 km, which isn’t really much by long-distance walking standards.