The programme ran from 1984 to 1996 and Shamir was Israel's PM from 1983 to 1984 and then again from 1986 to 1992. I'm guessing this programme went out some time in the early 1990s when apartheid still ruled in South Africa and the intifada was in full swing in Palestine.
Spitting Image was enormously popular in the UK and it's not surprising it has a lengthy Wikipedia entry. What is surprising is that this Shamir Mastermind appearance doesn't warrant a mention in the Spitting Image entry's International Politicians section:
No mention of Shamir. As it happens I couldn't imagine that piece appearing on UK mainstream television today what with comparing Israel unfavourably to apartheid South Africa and all but surely that makes it even more worthy of mention.Spitting Image lampooned US President Ronald Reagan (voiced by Frank Welker in the Ronnie and Nancy special) as a bumbling, nuke-obsessed fool in comparison with his advisors Edwin Meese andCaspar Weinberger. Next to his bed were red buttons labelled 'Nuke' and 'Nurse'. His wife Nancy was the butt of cosmetic surgery jokes.Mikhail Gorbachev had his forehead birthmark in the shape of hammer and sickle. All other Russians looked like Leonid Brezhnev, often said "da" ("yes") and talked about potatoes. In Russia it was snowing even indoors and the Soviet television had extremely low-tech visual effects.François Mitterrand was wearing a beret and a garlic wreath. P. W. Botha was shown as a racist cleverly disguising his views (once he had a badge "anti-anti-apartheid"). Adolf Hitler incognito had a house at9 Downing Street. Some appearances were also made by Idi Amin, Robert Mugabe, Ferdinand and Imelda Marcos, Ruhollah Khomeini, Saddam Hussein and Muammar Gaddafi.