From a European medieval reenactment perspective:
Weapon capable poison is seldom (~never) useful. So everything that works fine with your world of play is good, as it is unrealistic anyway. Assume a sticky sap, like syrup as the most likely form because everything else won't work. So to test how fast it decays: Use a kitchen knife and some syrup and cut some meat.
After that I need to rant something off:
TL;DR: Realistically an assassin would poison the food or cut the throat. But not poison the slit throat. Weapon poison is totally unrealistic, so looking for reasonable anything in that topic won't work.
Your realistic options by goal:
- Goal is to have your opponent dead NOW and you can come to close distance, a blade works better and more reliable then poison ever will. A club or an ax works fine too.
- Goal is to stun your opponent without killing him, grapple opponent from behind and hold mouth and nose closed until opponent fades because of the lack of air. Then bind and gag him quickly.
- Goal is a dead opponent and you can not come to close distance, a crossbow bolt to the chest is a good solution, it won't really become better with poison. Dip it in feces to make sure the opponent will die eventually if you miss the vitals.
- Goal is a dead opponent and you don't want to be attributable: poison his food or wine.
In medieval times you hire an assassin because you want to kill someone you can't remove (kill, exile, etc.) yourself. Usually one that you can't go to war with either (for political or financial reasons).
Your first course of action would be to have that person have a hunting accident. For that you bribe his assistant. Or alternatively you invite them for lunch and poison their food. For that you bribe your cook.
Only if both of this actions don't work and waiting is also bad and you have some connections into the criminal scene (which is unlikely for regular people, rulers or the nobility) and you have the money ready and you are comfortable that the criminal won't kill YOU instead to get your money; only then would you go seek an assassin. Alternatively you order one of your soldiers to do the kill, but they won't know proper poison either.
That means, work for assassins is few and far between, usually they are regular criminals not trained killers. Even today, assassins are usually ex-soldiers or regular criminals.
Criminals, on the other hand, have no use for poison because you can just kill the other guy with a knife or a club preferably when hes drunk. Simple, reliable, cheap, no fuss.
To further make my point: Have a look at the List of Poisonings. You will find lots of people who have been poisoned with their food and drinks but next to never with a weapon.
- Poison usually kills slowly. If you are in a fight, its of no use that your opponent dies three weeks hence from the poison. You want him dead now.
- If you want to kill without attribution, you poison his food. When he dies three weeks hence, no one will suspect that chicken he ate the other day.
- If its fine that your opponent dies in a few weeks after the injury, feces work fine and are dirt cheap. This is whats usually applied in medieval warfare to arrows as "poison".
- Animal poison needs to be applied in significant amounts, which is incredibly hard when not applied with a specifically designed weapon (like a syringe or snake teeth) that are not(!) useful without the poison.
- Most animal poisons that are poisonous enough to seriously effect a human, are stunning poisons. The animal that produces it wants its prey to be alive but not moving.
- Even if you did develop weapons that can realistically carry poison and you found a poison that does what you want and you are in a situation where you can apply it and it works out, you can't be certain that you used enough and on the right place etc.
I also recommend this comic panel for further ideas: SMBC