Your best weapon is the good old spear.
All the fancy poison, needle, special whatever need considerable skill, will wear off after some time, can be dangerous to the user and have a dozen other drawbacks.
Slashing or smashing weapons of any kind will leave considerable damage that is of interest to a reanimated corpse, i.e. bones and muscles.
Piercing weapons are intended to kill by puncturing vital internal organs - the thing that the walking dead don't have much use for.
Among the various piercing weapons, the spear has the greatest reach and flexibility, can be used to block or slash in case you need it, is relatively easy to learn, but can be deadly in the hands of a master. It also fits your specific type of immortals very well as most spear fighting styles depend more on speed and accuracy than on raw power.
Sure, you will want a dagger as a secondary weapon for any case and because it's useful to cut your lunch as well, but the spear will kill your enemies efficiently while leaving them useable for your dark magic.