Yes, it will be a token force - the United States only wanted British troops as a sign of their moral support for the war. The Conservatives, the Treasury and the Foreign Office all supported intervention.
Related to the issue of foreign affairs is the sterling situation, OTL LBJ offered the UK a blank cheque to support the parity of sterling if they contributed troops to Vietnam. Plus, the financial markets will be more favourable to a Conservative government. Sterling, however, was a residue of its historical value and devaluation would have to come eventually. Maybe slightly later in 1968/1969? In terms of economic policy, the Conservatives in the early 1960s no longer had prosperity to distract them from a genuine re-evaluation of their policies and were considering ways to modernise the economy. Throughout the 1950s there was considerable pressure on the Conservative leadership from backbenchers and pressure groups to prioritise lower taxes over high public expenditure. Modernisation would have to take the form of either cuts or incomes policy, pressure on sterling and defence commitments will probably result in significant cuts. Co-operation with the TUC is probably unlikely and increasing industrial unrest is probable with deflationary economic policies, leading to some restrictive trade union legislation, whether it would go beyond In Place of Strife I don't know. A form of economic planning had been adopted in the form of the NEDC in 1962, but as with OTL's National Plan it will probably be abandoned as it proves incompatible with deflation. The Conservatives would continue, I think, to press for EEC entry and may be successful if De Gaulle goes early. Macleod, Heath, Maudling, Hailsham and Soames will be key figures in the government.
A loss in 1964 will put Harold Wilson in a difficult position, he ran for the leadership as the self-proclaimed candidate of unity and had advanced a unifying ideology in terms of wedding socialism to the concept of scientific revolution. The discrepancy between his optimistic message and the reality of defeat will be clear. The Right will see the defeat as a vindication of the analysis they have made for years: that the weight around the party's neck is the Left's radicalism and obsession with nationalisation. Nevertheless the Right of the party won't have a clear figurehead to replace him, perhaps they will cast aside their doubts about George Brown or opt for Jim Callaghan. Roy Jenkins, Denis Healey and Anthony Crosland are all too inexperienced at this point. OTL in the 1963 leadership election, Wilson's victory was not assured at all, there was a strong possibility that Patrick Gordon Walker would run as the right's unity candidate and the PLP was dominated by the centre-right. If there is a leadership challenge to Wilson, I think it could go either way, perhaps with Wilson surviving, or a new leadership under Brown, Callaghan or Walker. Whoever is leader will probably win a general election in 1969. In many ways the outlook looks good for Labour, economic planning hasn't lost credibility through subjugation to sterling and therefore hasn't destroyed Wilson's unifying vision, they haven't alienated the trade unions and the progressive intelligentsia and students haven't left Labour as a result of the Vietnam War. In many ways the election of 1964 was a poisoned chalice.
I've considered doing a TL on this theme for a quite a while but I've never got around to it and need to do more research.