Well, I'm not sure if an assassine will contribute to the mood of a game. It is similar to a ghost appearance in a horror game, once you recognize, that it is not really a threat, the mood factor will drop immediatly. Nowadays it is even likely, that the player will hear from the ghost upfront (yes, I'm looking at you internet) , making the whole mood factor irrelevant.
I would try to connect it to some kind of gameplay feature, eg:
1. assassine as cause for some events
This goes into the direction of emergent game play. If an assassine attempt succeed, you are trouble. Eg you get hurt and are out-of-business for some turns leading to different internal powers trying to exploit it. The result could be a temporary chaos/anarchy (people dont pay taxes), riots (people damage buildings, killing an important minster) etc.
2. assassines as result of some effects
In this case you always caught the assassine and you get some information about its client. Eg the merchant guild dislike your decision to increase the tax on some goods, you can either try to execute the client, which have an exemplary effect on other factions, but you loose some important connections to the merchants. Or you could try to pour oil on troubled water to avoid getting in more trouble with the merchant guide.