It's obvious if you look at the content of the sealed letter, and at the fact the DF didn't dare use the proper channels (ie: give the letter to the Council of Nine or in Mayene to Berelain's people). A foreign ruler doesn't just go and ask the police forces of another nation to proceed to an arrest...

Bullying Domon or killing him wasn't enough, the Shadow needed access to his ship (possibly killing some of his crew was a long shot plan B to get him to hire new people, opening an opportunity to infiltrate a DF sailor to steal Domon's stuff).

Otherwise he was to be arrested at the Mayene harbor in very bizarre conditions (by a King who didn't dare petition the proper person to get his stuff back and instead left a sealed letter in the hands.... of the person he wanted to get arrested...), his possessions seized, and "Galldrian's men" would "unofficially" (ie: without petitioning Berelain as they should have if they were genuine representatives of the King) recuperate what was supposedly "theirs".

It's not spelled out but obviously they didn't have the resources to do this in Illian or anywhere else but in Mayene (for lack of DF in the right places, no doubt). It's very likely the DF came up with this plan simply because they happened to have someone among the relevant Mayene harbour officials who would get this letter and arrest Domon, seize his ship and possessions and discretely remove the seal from them, before the First of Mayene or her judiciary officials learned of it. When they did, if they did, they'd no doubt send a bird with pointed questions to Cairhien and Galldrian would deny everything (for real, but even had he been behind it he would have denied it anyway), and this would remain forever a mystery what Galldrian was so afraid would get in Berelain's hands that he didn't ask her, instead of her harbormaster, to give orders to arrest Domon.

It's doubtful in the extreme that the Council of Nine/King or the harbour officials in Illian would have agreed to give back something to supposed representatives of Galldrian without questions or without putting this in the hands of the Council of Nine first. or the Guild (Domon was a registered captain in Illian, not only a smuggler), especially since "Galldrian" didn't petition the Council as he should have and something fishy was obviously involved. It takes just a few days to get by pigeons a confirmation from the Sun Throne those representatives are no real representatives of the King of Cairhien, and it's them who would have been arrested instead of Domon.