It really wouldn't be hard to incorporate alchemy into an assassin's character. I've used it for all of mine, just because poisons are essential tools of the trade. If you want to RP accordingly, don't make any potions, just poisons. Eschew restore fatigue and health potions for drain fatigue and health potions. If you can find a drain speed or paralyse combination, more's the better. Alchemy might concern itself with flowers, but Nightshade, Stinkhorns and Wisp Stalks too.
Alternately, you might want to check out Shady Sam. Go behind the Handy Chestnut Stables at the Imperial City, and follow the walls to the left (if you're facing the Talos Plaza door, when you've come over the bridge). He'll be standing behind a buttress, selling all kinds of evil or illegal produce.