During a five-day tour of South-East Asia he will discuss "deepening relations across Asia" and "ensuring respect for human rights", according to the British High Commission in Kuala Lumpur, where he arrives tomorrow. The first is the standard diplomatic task of further warming generally cosy relations in a region which has strong historical, cultural and trading links with Britain.
The second relates to Labour's commitment to foreign policy with an "ethical dimension".
The challenge for Mr Cook is to frame his humanitarian concerns but avoid offending the sensitivities of his hosts at what, for several of them, is an unusually sensitive time.
In May Mr Cook was applauded by rights organisations after unveiling his policy a fortnight after taking office. Promising not to forget about "political values ... when we check in our passports on diplomatic business", he announced an annual report on human rights, an end to arms sales to repressive regimes, and "support [for] the demands of other people for the democratic rights on which we insist for ourselves."
But Mr Cook's decision to allow the planned sale of Hawk military aircraft to Indonesia disappointed many who had earlier praised him. Since then the new policy has found little practical expression.
Apart from an oppressive Internal Security Act (inherited from its British colonisers), Malaysia has one of the region's better rights records, although a court recently convicted a group of Muslim women for wearing bathing costumes at a beauty contest.
But Mr Cook's concerns are unlikely to get a sympathetic hearing from the Malaysian Prime Minister, Mahathir Mohamed, who recently called for the United Nations Declaration on Human Rights to be rewritten on the grounds that it was "formulated by the superpowers, which did not understand the needs of poorer countries."
Things will not be much better in Singapore, where a trial last week raised the question of political freedom.
JB Jeyaretnam, a left-wing opposition MP, is being sued for defamation by Singapore's prime minister after making factual statements at an opposition rally during last December's election campaign.
Mr Jeyaretnam's British QC, George Carman, last week accused the Prime Minister, Goh Chok Tong, of using the trial "as a method of causing financial oppression on this 71-year old man because you wanted him out of Parliament".
Earlier this year a US State Department report referred to the government's "attempts to intimidate the opposition through the threat of libel suits". Will Mr Cook support Mr Jeyaretnam, a left-leaning lawyer, like him? Or will he concentrate on building on Singapore's growing trade links with Britain?
The dilemma will be presented most acutely in Indonesia, whose numerous alleged rights abuses are seen by many campaigners as a test case for New Labour's policy.
Last weekend two tribesmen in the remote Irian Jaya province were said to have been shot, and others injured by Indonesian troops flown in to quell unrest at a copper and gold mine part-owned by a British company.