with full intel, i'd give it to Shikamaru, easy win.
with no intel, Haku with small chance that Shikamaru may survive.
since it is 1 vs 1. Ino-Shika-Cho is out of the question and so is the zabuza-haku combo as well.
with that being said, Haku can cast spells with one hand but can only use his extreme speed with in the mirrors.
he can also create a mirror wherever possible.
if shikamaru reacts quick enough and analyses that, he may actually win.
as for Haku, his only chance is if its a no intel.
Shikamaru with half intel managed to develop a plan to take out 2 akatsuki members with the help of his team ofc.
given full info of Haku's capabilities, he'd take the trophy.