Demonstrating the finesse of George Bush's political operation, the Jan. 16 get-together of all six Republican presidential candidates in New Hampshire will be more of a forum than a debate -- just as the vice president wanted, but without his fingerprints.

When representatives of the six met nearly six weeks ago, there was agreement the candidates would question each other at Dartmouth. But that arrangement was dropped from the proposal sent forward to the college's debate organizers by the state Republican Party.

Was this the fine hand of the Bush operation at work? If so, it was unseen. The vice president's men strenuously deny any involvement. ''There's no iron hand,'' national campaign manager Lee Atwater told us. Still, he can rejoice that the Dartmouth format bars Bush's pursuers -- certainly Gen. Alexander Haig, probably Sen. Robert J. Dole -- from hounding him about his role in Iran-contra.

Since cross-candidate questioning is a feature of other debates (including this week's in Iowa), the finesse in New Hampshire may be just a junior-grade coup. But it exposes differences between the political operations of Bush and Dole, his closest challenger. While Bush workers are monolithic in protecting their candidate, Dole's people are divided and ineffective about trying to put the front-runner in harm's way.

Actually, when the Dartmouth debate was first proposed last summer, the Bush forces wanted no part of a debate where the polls put them well ahead. Once it became clear that debate-ducking was impossible for this election, the Bush forces wanted to make the joint appearances more of a forum and less of a debate.

But when representatives of the six candidates met at state party headquarters in Concord Nov. 25, they objected to a feature consisting of answers to questions from Dartmouth students. They agreed on a format in which each candidate would be able to ask one question each to three of his opponents (drawn by lot). Ex-White House aide Andrew Card, representing Bush, did not specifically object, but said he would have to get back to his national managers.

That is the recollection of the meeting by several present, but not state Republican executive director Scott Malyerck, who presided. Malyerck, a political lieutenant of Gov. John Sununu (who is Bush's state chairman), told us, ''I don't remember if there was any agreement on cross-questioning.''

He certainly did not convey any such agreement to Dartmouth Prof. Richard Winters, in charge of debate arrangements. Malyerck expressed a desire for ''ample opportunity for candidate exchange'' in connection with questions from students, Winters told us, but nothing like the format agreed on Nov. 25.

What had happened was confirmed Dec. 10 when candidate representatives who had attended the Nov. 25 meeting received a letter from GOP state chairman Elsie Vartanian, another Sununu lieutenant. In what was supposed to be a ''review'' of what had been discussed, the candidate-to-candidate questioning stressed two weeks earlier had disappeared from her letter.

Operatives for candidates Jack Kemp and Pierre du Pont now have drafted a letter to Vartanian, dated Jan. 5, to be signed by all who attended Nov. 25 and reasserting their agreement on cross-candidate questioning. Not surprisingly, Card declined to sign. More surprisingly, the Dole campaign did notimmediately join representatives of Kemp, du Pont, Haig and Pat Robertson in signing the letter.

Jim Carroll and Paul Jacobson, Dole's operatives present Nov. 25, did not contest the agreement as described in the Kemp-du Pont letter, but felt this was something for national headquarters to decide. The decision there probably will be no. Former New Hampshire attorney general Tom Rath, a senior Dole national campaign adviser and, coincidentally, Dartmouth counsel, told us, ''I don't fear that this is being pressured'' by Bush and added he is not high on structured candidate-on-candidate questioning.

But other Dole advisers feel Bush must be pressed on the Iran-contra connection and that the senator cannot rely on Haig to do his dirty work. If Dartmouth turns into more of a forum than a debate, there will be one less major opportunity to slow down the front-runner.

The incident is a study in contrasts. The Bush campaign has been focused on the Dartmouth debate format and what was in the candidate's best interests, with Atwater on top of the dispute. Not so the Dole camp. Atwater's counterpart, campaign manager William Brock, was finishing a 10-day Caribbean vacation, and his surrogates did not come to grips with how to win the edge for their man in a potentially crucial debate.