It depends on the neuro exam. Are you able to tell us more about this? Ultimately, the CT is useful, for the uninitiated - the CT is c/w anoxic injury, but hardly definitive for prognostication.
Now, if he is completely unresponsive and is left with only a corneal reflex on the left, for example, then it is time to have a sit down with family. But, if he is posturing, or otherwise doing "something" then I would move ahead aggressively. Regardless, a cEEG is useful because anoxia often results in seizures and this may cloud your exam and be treatable. Also, if he is in myoclonic status then that information is very useful as well.
I prefer HTS, either 3% or 23.4% to mannitol. Reason being, there can be some ICP rebound with mannitol and often I don't want the patient to be diuresed.
Lastly, I would avoid hyperventilation for treatment of elevated ICP unless you plan to do it only breifly (i.e. on the way to the OR for decompression) and the patient is actively herniating. The effect of hyperventilation is quite temporary as the initial vasoconstriction is overcome by cerebral autoregulation resulting in a significant rebound effect. Keep PCO2 normal.
Cheers,
iride