Not really, we are once again over-egging the Hunter and ignoring the size shrinkage of the nuclear weapons available to the RAF. The Hunter replacement aircraft clearly had to have a credible nav-attack system (they are needed for conventional strikes to) and an element of defensive electronic systems- so a radar warning receiver. In addition the aircraft would almost certainly have to be supersonic. From a survivability perspective the assumption appears to have been that the Soviet client states would get 95% of what the WarPac forces would get. Furthermore, carrying a WE177 was considerably less arduous than dragging around Red Beard, in fact WE177 was only about 1,000lbs meaning that its carriage had only a limited effect on the aircrafts design (mostly related to wiring and cockpit layout); see carriage by both the Jaguar and Sea Harrier. The primary driver in the aircrafts complexity and weight would have been unrelated to the nuclear role. Whilst it is of course absolutely true that the Hunter replacement had to carry a small nuclear weapon (in large part to offset the 50% cut in the size of 2nd TAF- RAFG from 1959- that came out of the 1957 White Paper), it is not necessarily the case that this decision became a major driving force behind the aircrafts design.
The RAF, in typical fashion, ended up using whatever was available for the out of Europe role- but the vast majority of both the Harrier and Jaguar fleets were deployed to RAFG (3/2 and 5 squadrons respectively). The Hunter FGA-9 was absolutely developed to replace the Venom, but the relative lack of advancement between the two (The Hunter only really added some marginal range, speed and payload enhancements) meant that obsolescence arrived quite rapidly.
For me there is one major outstanding question relating to the Hunter FGA-9/FR10 replacement in its P.1154 guise and that is what exactly the fighter capability of the type would have been. Harriers website mentions that the aircraft was to carry Red Top and BSP states that a 21 inch version of the AI23 would have been used. I assume it wouldhave been interfaced with the Ferranti INAS which later made it onto the Phantom and Harrier; according to BAe/McDonnell Douglas Harrier by Andy Evans the INAS was 'one of the major items received' from the P.1154 project. However, 21 inches makes for a diminutive radar, by comparison even the puny variant in the Lightning was 24 inches whilst the Phantom had 32 inches! It is true that in the Lightning some fancy things were done by integrating the radar into the auto-pilot (AI-23B) and even more fancy integration was considered, a fully auto-attack system was apparently test flown though never put into production despite a £1.4 million investment, there was a datalink as well. I am also assuming that the AI-23 variant used would have been the Ferranti AIRPASS Mk2 that Ferranti was marketing in the early 60s and I believe was specified for export Lightnings as well as being offered with some other European aircraft of the time (did it ever make into RAF Lightnings?) as it was designed as a multirole radar (was first shown publicly in 1962).* However, it still seems that for an aircraft entering service in 1970ish the small AI23 and Red Top combination would be dubious (Seeing as this is an alternative history thread we can now see a path to the proposed Mk 2 Red Top mentioned in BSPIV?, possibly even a Blue Dolphin version with the Marconi XJ.521 from Skyflash?).
* http://www.flightglobal.com/pdfarchive/view/1960/1960 - 1430.html?search=Ferranti AIRPASS Mk 2
