I'm trying to remember the name of an alternative-history short story, can anyone help me? It is about a man who refuses to drop a bomb because he feels that he would be responsible for the deaths that followed, though he was not the one that placed the order. He begins to question culpability. Later he is executed and he wonders if the riflemen know which one will kill him. It may have been written by a woman.
This sounds like "The Lucky Strike" by Kim Stanley Robinson (actually a man, but often mistaken due to his first name).
It's an alternate history tale in which the pilot of the Enola Gay, the plane that dropped the bomb on Hiroshima, died in a crash just before the mission, and a different, more conflicted man, took his place:
"I know," said January. He was still in shock, in imagination crushed, incinerated, destroyed. Once as a kid he had tied sheets to his arms and waist, jumped off the roof and landed right on his chest; this felt like that had. He had no way of knowing what would come of this crash, but he had a suspicion that he had indeed smacked into something hard.
Scholes shook his head. A half hour had passed, the fire was nearly out. January's four mates were over chattering with the Seabees. "He was going to name the plane after his mother," Scholes said to the ground. "He told me that just this morning. He was going to call it Enola Gay."
This new man, January, doesn't believe it's right to drop a bomb on civilians:
January's knee vibrated against the squat stand of the bombsight. He was the one who had to drop the bomb. No matter where his thoughts lunged they were brought up short by that. He was the one, not Fitch or the crew, not Le May, not the generals and scientists back home, not Truman and his advisors. Truman—suddenly January hated him. Roosevelt would have done it differently. If only Roosevelt had lived! The grief that had filled January when he learned of Roosevelt's death reverberated through him again, more strongly than ever. It was unfair to have worked so hard and then not see the war's end. And FDR would have ended it differently. Back at the start of it all he had declared that civilian centers were never to be bombed, and if he had lived, if, if, if. But he hadn't. And now it was smiling bastard Harry Truman, ordering him, Frank January, to drop the sun on two hundred thousand women and children. Once his father had taken him to see the Browns play before twenty thousand, a giant crowd—"I never voted for you," January whispered viciously, and jerked to realize he had spoken aloud. Luckily his microphone was off. But Roosevelt would have done it differently, he would have.
So, when the time comes, he decides to deliberately delay dropping the bomb by faking a glitch:
Deliberately he took a breath, held it. Clouds swam under the crosshairs, then the next island. Almost there he said calmly into his microphone. "Steady." Now that he was committed his heart was humming like the Wrights. He counted to ten. Now flowing under the crosshairs were clouds alternating with green forest, leaden roads. "I've turned the switch, but I'm not getting a tone!" he croaked into the mike. His right hand held the switch firmly in place. Fitch shouting something—Matthews' voice cracked across it—"Flipping it b-back and forth," January shouted, shielding the bombsight with his body from the eyes of the pilots. "But still—wait a second—"
He pushed the switch down. A low hum filled his ears. That's it! It started!"
And it of course misses it:
January looked. The cloud layer below had burst apart, and a black column of smoke billowed up from a core of red fire. Already the top of the column was at their height. Exclamations of shock clattered painfully in January's ears. He stared at the fiery base of the cloud, at the scores of fires feeding into it. Suddenly he could see past the cloud, and his fingernails cut into his palms. Through a gap in the clouds he saw it clearly, the delta, the six rivers, there off to the left of the tower of smoke: the city of Hiroshima, untouched.
"We missed!" Kochenski yelled. "We missed it!"
January turned to hide his face from the pilots; on it was a grin like a rictus. He sat back in his seat and let the relief fill him.
But they don't buy that it was an accident:
"Is that right?" Fitch cried, as angry as Shepard. "Did you screw up on purpose?"
"No," January grunted, and knocked Fitch's hands away from his neck. He swung and smacked Fitch on the mouth, caught him solid. Fitch staggered back, recovered, and no doubt would have beaten January up, but Matthews and Benton and Stone leaped in and held him back, shouting for order. "Shut up! Shut up!" McDonald screamed from the cockpit, and for a moment it was bedlam, but Fitch let self be restrained, and soon only McDonald's shouts for quiet were heard. January retreated to between the pilot seats, right hand on his pistol holster.
The city was in the crosshairs when I flipped the switch," he said. ‘But the first couple of times I flipped it nothing happened—"
"That's a lie!" Shepard shouted. "There was nothing wrong with the switch, I checked it myself. Besides, the bomb exploded miles beyond Hiroshima, look for yourself! That's minutes." He wiped spit from his chin and pointed at January. "You did it."
"You don't know that," January said. But he could see the men had been convinced by Shepard, and he took a step back. "You just get me to a board of inquiry, quick. And leave me alone till then. If you touch me again," glaring venomously at Fitch and then Shepard, "I'll shoot you." He turned and hopped down to his seat, feeling exposed and vulnerable, like a treed raccoon.
The ending also matches pretty closely to what you describe:
And with that he relaxed. In his last week everyone who met him carried away the same impression, that of a calm, quiet man, angry at Truman and others, but in a withdrawn, matter-of-fact way. Patrick Getty, a strong force in the January Society ever after, said January was talkative for some time after he learned of the missed attack on Kokura. Then he became quieter and quieter, as the day approached. On the morning that they woke him at dawn to march him out to a hastily constructed execution shed, his MPs shook his hand. The priest was with him as he smoked a final cigarette, and they prepared to put the hood over his head. January looked at him calmly. "They load one of the guns with a blank cartridge, right?"
"Yes," Getty said.
"So each man in the squad can imagine he may not have shot me?"
"Yes. That's right."
A tight, unhumorous smile was January's last expression. He threw down the cigarette, ground it out, poked the priest in the arm. "But I know." Then the mask slipped back into place for good, making the hood redundant, and with a firm step January went to the wall. One might have said he was at peace.