What Mad Universe, a 1949 novel by Fredric Brown; a shorter version, originally published in Startling Stories, September 1948, is available at the Internet Archive.
It has your hero traveling (involuntarily) between parallel Earths; in the "other" universe the Earth is under attack by aliens from Arcturus. Your dangerous criminals with tapping canes are called Nighters.
Excerpt:
And then there was another sound, a new one. It was a different kind of sound altogether—it was the distant, soft tapping of a hundred blind men's canes. As though a company of blind men were coming tapping through the dark. The sound came from the direction in which Keith had been going, the direction of Broadway and Times Square.
He heard a subdued mutter, "Nighters!" and then the quick shuffle of footsteps as his former assailant started off. His voice, no longer cursing or even belligerent, came back out of the dense dark: "Run, pal. Nighters!"
The shuffle and scuffle of his footsteps died away as the tapping sounds got louder and nearer. They came nearer incredibly fast.
What were Nighters? Human beings? He tried to piece together the few things he'd heard about them, or read about them. What had the man with the scarred face said about them?—"They go in armlocked gangs from building to building and you can hear 'em tapping." Human or otherwise, they must be an organized gang of killers that scoured the streets of the mistout—a long row of them from building to building with their arms locked together, tapping canes to guide them.
[. . . .]
Two lines of them, coming from opposite directions, and he was in between. That was their method of hunting, of treeing whatever quarry might be on whatever block they were working. He'd wondered how they managed to catch anybody when their progress by tapping gave them away and warned their quarry to run. But he understood now.
He stopped, his heart beating wildly. The Nighters—whatever Nighters were—had him in the middle. There was no way to run.
Wikipedia synopsis:
Keith Winton is an editor for a science fiction magazine, working during the late 40s when genre fiction magazines have not yet given over to TV shows. With his glamorous co-worker, Betty (an employee of the 'romantic stories' magazine, on which he has an undeclared crush), he visits his boss in his elegant estate in the Catskills, unfortunately on the same day as an experimental rocket laden with a high-voltage generator able to be seen discharging on the Moon's surface is to be launched. Betty has to go back to New York.
Keith is alone in his friends' garden, deep in thought, when, suddenly, the rocket's generator (whose launch has been a failure) crashes on his friends' residence and dissipates its gigawatt electrical charge right on the spot Keith is standing on. The massive energy discharge allows his physical form to 'shift' through dimensions, taking him to a strange but deceptively similar parallel universe.
At a superficial glance, the streets look the same, there are the same kind of cars and the people wear the same kind of clothes (and he also knows some of the people, though sometimes they don't know him), and the radio broadcasts familiar tunes from the Benny Goodman Orchestra. But there are many incongruous elements in this seemingly familiar reality. Wild-eyed, Keith is astonished to see how credits have replaced dollars; is amazed when he encounters some scantily-clad pin-up girls who are, at the same time, astronauts; is driven to stupor when he encounters his first lunar native vacationing on Earth. Then, he discovers, to his cost, that such an innocent activity as coin collecting could lead to being suspected of being an Arcturian spy—and since Arcturians possess awesome mental powers and are bent on exterminating humanity, any such suspicion is liable to lead to being shot on the spot. And managing to escape the spy scare, he finds that New York has no night life; there is a total, impenetrable darkness, and wandering the completely dark Times Square could lead to a fatal encounter with the terrible Night Men . . .
Having as a science fiction editor rather despised space opera, he finds himself living in a "Mad Universe" where the most cliché aspects of that subgenre are an actual, daily reality. In order to have any hope of getting back to his own world, he has to get in touch with the impossibly 'larger than life' hero who leads Humanity's struggle against the Arcturian menace and his "artificial brain" sidekick Mekky, getting involved in a desperate last-minute plan to thwart the onslaught of a fearsome alien superweapon against the Solar System and Earth.
At first inclined to regard all this as a bit far-fetched, he is reprimanded by this world's version of his beloved Betty: "Do you think the danger of all humanity being exterminated is a matter for joke?" In the end, he has no choice but himself assume the role of a dashing space hero, embarking on an almost suicidal single-handed attack on the terrible alien ship.
