TATP fully detonates without air. It's a high explosive (5300m/s). Only the complete combustion would need additional oxygen, what does not happen in the detonation (but the initial TNT-like detonation then transforms the reactor's contents in an air-breathing bomb, and may detonate the concentrated hydrogen peroxide as well).
The Wiki article seems voluntarily botched. The London bombings were carried using TATP.
In your risk analysis, will you detonate some TATP too see what happens then? To get an intuitive idea of how sensitive and powerful it is. Better try a tenth of a gram before having tons.
From the linked Pdf, second paragraph:
"TATP is one of the most sensitive explosives known" and
"with power close to that of TNT". This does of course not rely on additional air.
Beware the linked Pdf has only estimated the heat of formation by
software. More serious sources measured +91kJ/mol and +151kJ/mol - and this does not include the partial combustion, for instance 6* 110kJ/mol for the CO, unless you do believe that a detonation produces ozone besides hydrocarbons.
Primary Explosives, By Robert Matyáš, Jiří Pachman (available from Google Book)
and
http://onlinelibrary.wiley.com/doi/10.1002/prep.201100100/abstractMaybe you could drag Anders Hoveland in this conversation, if he's still reachable? He has practical experience with explosives, at least in lab amounts.