Ravenous Hydra or a Statik Shiv? It's for my Tryndamere, since he's a bit weak without champion kills, so I guess farming would be the second option.

Ravenous Hydra without a doubt. Continuous AoE damage. Stattik Shiv is a slightly weaker version of a Phantom Dancer with one added benefit; AoE magic damage at 100 charges. The only problem is that this AoE nuke only hits 4 enemy units. Also, the effect targets enemies at random, where Ravenous Hydra's passive will just tear away at anything around you.

Rabadon's deathcap. Dat spinning slash AP ratio

If you require a selection between the two I'm going to say Statik for 2 reasons: I think it's cheaper than Hydra, and it boosts attack speed. I really don't like statik much for Trynd, though, since it adds crit chance.

However, if you are willing to accept suggestions, Madred's Razor into Wriggles. The razor's chance to deal a massive blast of damage to minions and monsters make it amazingly useful in tearing through creeps. Whenever possible, I recommend damage and attack speed over crit chance since Trynd is able to get such a high crit chance naturally, but of course it all depends on what your preference is.

Shhhh, don't confuse him. X)

Ravenous Hydra because of timat effect and lifesteal is great on Tryn. Also, i'd recommend as others have said Phantom Dancer over stattik shiv on Tryn because of the att speed + critical strike is great on him.