Reviewing some more recent sources, Danny Orbach in Curse on this Country, his work focusing on gekokujōin the Imperial Japanese Army has the following narrative for Prime Minister Okada's fortunate escape:

Lieutenant Kurihara Yasuhide spearheaded the effort to “eliminate the traitors,” the dignitaries whose mere existence made restoration impossible. The most important of these “traitors” was undoubtedly Prime Minister Okada Keisuke. At 5:00 a.m., Kurihara’s squad arrived at the prime minister’s official residence. Kurihara posted armed soldiers at every exit, and broke into the apartments with his troops. While some of the invaders were fighting the guards, others searched for Okada in the corridors. They didn’t have prior intelligence about the contours of the prime minister’s sizable residence. When the house staff disconnected electrical power, the invaders had to feel their way in the dark. In the garden they spotted a man in night clothes, Okada’s brother-in-law, and shot him. Kurihara examined the slain man and, mistaking him for the prime minister, ordered his soldiers to surround the residence and block all access. From there, he hurried to the army minister’s residence. In fact, Okada had been hidden in a closet by one of the servants and was eventually whisked out of the building.

His sources are from Ambassador Grew's cable back to the State Department on how the Prime Minister Okada escaped assassination, as included in Grew's personal papers and diaries. S.C.M Paine in The Wars for Asia also reports on Okada's survival due to the assassins mistaking him for his brother-in-law, citing two secondary sources. Neither of these make a reference to his wife helping him escape, and since the only example available is unsourced, I'm inclined to believe that the "mistaken for his brother-in-law" narrative is more accurate, since for this we do have a primary source.

I do wonder however, if the mistake is conflating Okada's escape with the survival of Grand Chamberlain Suzuki Kantarō, who was wounded in the assassination attempt by the rebel soldiers, but ultimately survived as his wife persuaded the soldiers to depart without striking his body with their swords. Similar stories exist with Count Makino Nobuaki, who escaped from the ryokan he was staying in, via help from a police officer, a nurse, and his graddaughter, as well as with former Prime Minister and Lord Keeper of the Privy Seal, Saitō Makoto, whose wife Haruko attempted to shield him with her body and requested to be killed in his place. Haruko was pushed aside and Saitō killed by close range gunfire. With multiple incidents of the wives of those targeted for assassination intervening to try and save the lives of their husbands, it's not surprising that there may have been a mistake somewhere, with Okada's survival attributed to the actions of his wife.