When it first advertised in 1971 a handgun "Just for the Ladies," Charter Arms Corporation, a Connecticut firearms firm, called it "The Undercoverette." It was to be for women what "The Undercover" was for men: a light but hard-blasting quality weapon able to get the job done. John Lennon's killer used an Undercover, as did George Wallace's attacker.

Charter Arms no longer uses the name Undercoverette. An official explains that because a fair number of men have come to like the palm-fitting marvel, the feminine linkage isn't a marketing advantage. In tough-guy circles, apparently, packing a woman's rod tends to dampen the macho factor.

So now it's a unisex gun, though Charter Arms still markets it with women in mind. Happily so. These are boom times in the arming of American women. The fear of crime, combined with a sense of unprotectedness among women who live alone, means that the handgun is no longer a men-only weapon.

Evidence of this surprising development is not hard to find. In Massachusetts, Gun Owners Action League reports that between 15,000 and 20,000 women are signing up for instruction in handgun use this year. Double that number, it adds, have been applying for handgun licenses.

In Atlanta, Edwin Topmiller, a National Rifle Association director and a man who sleeps with a 20-inch barrel 12-gauge pump shotgun next to his bed, estimates that in the past seven years he has taught 2,500 women how to use firearms. The demand grows, he says, with as many as 40 women per class.

In Rhode Island, the Providence Journal reports that "at least one of every four new owners of a handgun is a woman." A National Rifle Association official in Washington says that his group may soon approach the National Organization for Women to offer the latter whatever firearms expertise its membership may want.

This being National End Handgun Violence Week, organized in 300 events across the country by the National Coalition to Ban Handguns, the question begging to be answered is just how effective this call to arms is likely to be. Will the meet-violence-with-violence ethic mean that the gun-toting woman is better protected than her non-gunner sister? Will it mean an increase in actual safety or only an increase in the illusion of safety?

The effectiveness debate was raging long before women were putting revolvers in their purses. It has been a debate that the gun lobby -- from its strident "right-to-bear-arms" zealots to cowering politicians fearful of offending the NRA -- has forfeited to reasoned advocates like Michael Beard of the Coalition and Pete Shields of Handgun Control.

Shields in "Guns Don't Die -- People Do," an eloquent and persuasive book, states that "citizens aren't noticeably safer when they have a handgun. Facts show that a handgun kept for self-defense is far more dangerous to its owner and his family than it is to the criminal. There are far more accidents and acts of passion with one's own handgun than there are either criminal murders or preventions of criminal attack."

The National Safety Council reports that 1,800 citizens were killed in firearm accidents in 1978.

Opposite Shields and Beard is Mike Usino of Gun Owners Action League. Accidents do happen, he agrees, but "let's not use numbers to guide our lives. If an individual feels safe -- that carrying a gun is his security blanket -- then that should be his choice."

The feeling of safety is a new twist in the debate. It means, evidently, that if a person feels insecure without a loaded revolver on the night-table -- or glove compartment, hip pocket or purse -- then everyone around him must live gingerly, ever-ready to duck fast when the shootout comes.

It means that Michael Beard's assessment of the bloodshed may soon be obsolete: "If you own a handgun, or live with someone who does, you're twice as likely as the average American to be murdered, accidently shot or to commit suicide."

Meanwhile, the women's market grows. With no Undercoverette so named, why doesn't a manufacturer come out, say, with a Jean Harris Lover's Spat model, or perhaps a Nancy Reagan When Ronnie's Away .38?