With the exception of Daggers.
It depends on the fantasy surrounding what an Assassin is.
Stealthy and sneaky, being able to blend in with surroundings and crowds would be an assassins most potent ally. Having a hidden blade would be ideal for this, as larger weapons such as swords would be easier to pick out.
If the thought process is more rogue-like, having a short sword would be acceptable. In the end, everything would need to be able to be concealed somehow either under cloak or some other method.
For ranged, throwing knives or small explosives such as poison bombs or smoke bombs. However that moves into more of a ninja niche.