How does Perplexing Chimera work with multiple triggers on the stack?
Quoting directly from the Born of the Gods Release Notes:


  In some unusual cases, you may not control Perplexing Chimera when its triggered ability resolves (perhaps because the triggered ability triggered again and resolved while the original ability was on the stack). In these cases, you can exchange control of Perplexing Chimera and the spell that causes the ability to trigger, even if you control neither of them. If you do, you'll be able to change targets of the spell, not the spell's new controller.


Note that, because both Perplexing Chimera and Shock are controlled by your opponent when the first triggered ability resolves, exchanging their control doesn't change anything by itself, but it does give you (yes, you, even though you still don't control anything) the option to change the Shock's target.

I'd also like to quote another item in the section on Perplexing Chimera which addresses a misconception you seem to have:


  You make the decision whether to exchange control of Perplexing Chimera and the spell as the triggered ability resolves.


That is, the triggered ability goes on the stack regardless of whether you want to make the exchange at that time; you don't decide whether or not to do the exchange until the ability resolves.