In order to make this non-ASB one has to ask: how does Israel conquer the WB/Gaza? It's not so simple as just deciding to do it. Historically the chance to conquer WB/Gaza came in the autumn of 1948, but it was a choice between trying to do that (with success not guaranteed; the Jordanians were feisty) or striking against the substantial and arguably more dangerous Egyptian position in the south. Benny Morris' book 1948 discusses the situation in chapter 7. Ben-Gurion wanted the WB but his Cabinet voted 7-5 against it. (Ben-Gurion called this a 'bechiya ledorot', 'cause of lamentation', which would actually make a good TL title.) Two significant considerations were:
1. the WB was not allocated to Israel under the UN Partition Plan, whereas the Negev was, and in the aftermath of the Bernadotte assassination there was a risk of diplomatic isolation;
2. there were besieged kibbutzim in the Negev.
It would not be too hard to butterfly both of those - i.e. evacuate the Negev kibbutzim before the Egyptian invasion, and save Bernadotte by some chance (e.g. suppose that the plane on which he flew on 17th September couldn't make it and returned to Rhodes with engine trouble). In those circumstances, the narrow Cabinet vote might go the other way. But before going on to think about long-term effects there are major short-term ones. If operation Yoav goes east instead of south, that leaves the Egyptian army in the south unmolested, and maybe means that Israel does not get Beersheva or Eilat. A costly victory over the Jordanians makes major problems for Israel diplomatically - one can't even rule out British intervention to help the Jordanians, if London felt there was a risk that defeat meant Abdullah being overthrown. If British intervention and/ or Abdullah losing power did happen then you've got a major butterfly to deal with. Finally, one can't necessarily assume that the WB Arabs will all become refugees, that wasn't the case, for example, for the Arabs of the central Galilee which Israel conquered at about this time (operation Hiram, end of October 1948).