Unless anything changed in the FAQ, taking an additional hand weapon means you don't get poison on either.
Why? It is not something like Obsidian Blades that stipulates handweapons, if you just have the poisoned attack special rule all your attacks, except magical weapon attacks, gets them.
Poisoned Attacks
Deadly toxins can turn an otherwise minor
injury into a mortal wound.
If a model with Poisoned Attacks rolls
a natural 6 when making a roll To Hit,
that hit will wound automatically. Unless
otherwise stated, a model with this special
rule may use it when making both shooting
and combat attacks. Any spells cast by the
model are unaffected, as are any attacks
made with magic weapons.