Yigal Amir misses by a couple centimeters. Rabin gets wounded but makes full recovery. The "they killed our prime minister" shock still exists as in OTL, to some extent, but the candidate in the 1996 election is Rabin rather than eternal loser Peres, and at the end Rabin squeaks by and is reelected.
The problem is that Barak is still poised to be Rabin's successor at this stage, and he's not going to be better than in OTL...
(Honestly, Peres lost by so little, and was up in the polls until shortly before the election, that he might have won anyway - it boiled down to last-minute campaigning decisions, like Bibi's "Peres will divide Jerusalem" campaign.)
Trying to postpone the 1977 election results isn't going to change much. Eventually, in a democracy, the ruling party loses. The interesting bit isn't that Labor eventually lost - it's that since 1977, the only period of recognizably center-left government in Israel was 1992-1996. A lot of it has to do with the Russian migration wave rather than the Mizrahis. In the 1990s, the Russians were the bellwether group. They drifted right in the 2000s, due to issues like "Labor and Meretz dropped the ball on talking to them rather than at them" and "Lieberman's popularity grew."