No.
No.
No.
No.

Because they are not madreds bloodrazor or wriggles or blackcleaver

hextech: AP is alright on shaco but not that great, if you want physical damage, black cleaver proc works with your clone and it's very effective. Wriggles better for jungling and you already get lifesteal from there.

Trinity: cos its good all around, it could WORK but it's not really cost effective for shaco. Really really expensive item.

Nashors: For shaco, the cdr/AP/mana regen is not worth the cost (compared to getting damage items). AS is alright but you can do better from other sources.

SotD: getting pure AS is pointless if you dont have on hit effects to make use of it (and its own passive is not really enough to justify that). That's why you see a lot of these on xin zhao, but not so much on other champions.