If Ranma is worrying that the arrest of Bengtsson would be considered "arresting your opposition" - make the trial public (or as public as it can be), with the accused being able to speak in his defense, and perhaps with someone speaking on their behalf (like the advocate).
Though I don't know what is Japanese view on secret courts...
Wow... You're asking some very difficult questions here...
While Ranma did arrest his opposition, he didn't kill them like many dynasts would have (i am pointing the view of an outsider not what Ranma is thinking). And i think he's going to play on the angle of any crimes not related to the overhtrow of his position, that is the kidnapping of Sun Ya mainly.
As for the son of Bengtsson, Ranma did ask them to disperse first before non-lethaly dispatched them. When the soldiers stories of his first battle in Greyfall and this will reach the popuation, his star will rise again. Ranma doesn't use honeyed words, like the immaculate warned the people against the anathema, but actions that speak more loudly and effectively.
And all this is without taking into account her unconscious use of Solar charisma.
The Public trial is no go because they need to prepare Greyfall against invasion rapidly. Ranma would certainly call all the leaders to assist such a trial, but i can see him waiting for the end of the invasion crisis.
As for the Japanese view... Perhaps are you refering to the old laws (samurai era) when the rank and sincerity of the accuser and defender were the decisive factor in a trial?
Until 1868, the Japanese criminal justice system was controlled mainly by the local daimyos. Public officials, not laws, guided and constrained people to conform to moral norms. In accordance with the confucian ideal, officials were to serve as models of behavior.
The people, who lacked rights and had only obligations, were expected to obey. Such laws as did exist were transmitted through local military officials in the form of local domain laws. Specific enforcement varied from domain to domain, and no formal legal codes existed. Justice was generally harsh, and severity depended upon one's status. Family and neighbors could share blame for an offender's guilt: whole families and villages could be flogged or put to death for one member's transgression.
Modern Japanese law: Three basic features of Japan's system of criminal justice characterize its operations.
First, the institutions (police, government prosecutors' offices, courts, and correctional organisms) maintain close and cooperative relations with each other, consulting frequently on how best to accomplish the shared goals of limiting and controlling crime.
Second, citizens are encouraged to assist in maintaining public order, and they participate extensively in crime prevention campaigns, apprehension of suspects, and rehabilitation programs.
Finally, officials who administer criminal justice are allowed considerable discretion in dealing with offenders.