I'd say you've got a couple of options here.
The first is to use
Yanfly's weapon Unleash plugin, and make the buff set your attack skill to a different skill, one that looks like a normal attack, and then also does poison damage (using action sequences). You'll probably have to throw at least one eval command in there to set the element of the added poison effect to something that isn't the same element as your physical attack, maybe swap the hit type from physical to magic, or certain hit, to stop the second effect from missing as well.
The other option is to use Skill Core, in combination with Buffs and States Core to use a <Custom Confirm Effect> or a <Post Damage Eval> to cause a forced action to occur when the buff is active on a battler. This is a lot more complicated, and you'll have to build in checks to stop the added skill from triggering off of itself, or it'll cause an infinite loop. There was
a topic with something similar that I assisted in a few days ago which is relevant, but since it's a little different than your exact use-case, it'd need to be modified to work.