It takes experience to decide on whether or not split-pushing is your best option. It's true that a lot of players (and not just in silver) don't know how to play with a split pusher; you have to factor this in to the decision of whether or not to split push. Sometimes you'll get games where your team communicates fabulously and even calls out "1 3 1, me top, shaco bot" and it works like a charm. The other thing to consider is...sometimes split pushing is your only/best option. If you haven't snowballed the game in your team's favor, and the enemy team is a malphite/lissandra/leona/amumu....you probably can't teamfight them. You could go for a lot of map vision and look for picks, but if the enemy team stays grouped and/or their vision control is better than yours, split pushing and hoping they make a rotational mistake is probably your only option.
In terms of building Shaco - ravenous hydra is obviously the core item. Warrior is not bad either..it is a very stat efficient item, and unless you have a lot of gold on your first back, it's almost always worth it to get the ranger's trailblazer upgrade. It gives you more gold and more sustain/better clear, ESPECIALLY if you plan on giving blue buff to your mid laner. Statik shyv is nice because the passive can crit off your Q, and the atk speed and mobility helps you.
Here's the thing though. Don't be afraid to get some survivability in there. Hexdrinker is a must vs. a fed burst mage. I get merc treads or ninja tabi more often than I get mobi boots - it's a very stat efficient way to get some survivability against whichever the most important target is for you to kill. And I almost always get black cleaver on shaco. It's true that the armor pen isn't the best thing in the world for shaco, but the CDR helps you get that extra Q or W and the health helps you barely survive those close calls.
I'm no shaco expert...I'm a Plat player but whenever I play shaco in normals vs. golds I usually stomp using the above itemization and strategy. My final build is usually hydra, statik, black cleaver, boots, Maw, phantom dancer. I get phantom dancer as a last item becuase if the game goes that long, it gives me a powerful presence of being nearly uncatchable (remember as shaco you don't have flash) so I have the option to split push a well as stick to my targets if I decide to duel or teamfight.
Hope this helps! I too find him a fun champion, and wish so much they would simply give some QoL buffs on his clone. I love his kit otherwise, and the style of play it requires. It's much more decision making than mechanics.