I have only one observation of my own to add. Living in London, I am not near a large mega-mart and garden centre and have only limited access to firearms. My options for an extended fortified siege are limited, even now I can foresee it will be necessary for me to walk amongst them.
Zombies are a lot worse at passing themselves off as humans than Dan Dennett would have you believe. There is no known incident of a zombie passing the Turing Test. (Certainly none I have seen published in a peer-reviewed journal.) Often, zombies are detected almost instantaneously due to their obvious lack of social awareness or other simple and striking non-verbal cues. An alert human will have no difficulty discriminanting between zombies and non-zombies.
A more interesting question is, how easy is it for a human to pass as a zombie? There is a well documented history of zombies not attacking each other. The reasons for this are unclear, but a working hypothesis is that they can make the basic perceptual discrimination between living and undead. Certainly this would be beneficial to them, for as the old saying goes "Consciousness is an epiphenomenon of fresh brains."
This leads us to speculate as to what form of perception zombies use to detect humans and whether we can fake it. The zombie state is almost synonymous with higher-cortical disfunction; they lack language and expressive behaviours, they show no purposeful action and extremely limited abstract reasoning ability, they show only primitive fears of fire, etc. They do seem to possess some primitive procedural memory, some kind of instinct, memory of what used to be but do not demonstrate the ability to assimilate new information or learn new skills.
Therefore, it seems likely their higher sensory apparatus will also be working on a similarly degraded level and the potential for deception exists. As is true of some much of perceptual psychology far more is known about the visual system in zombies, than other senses. Even leaving aside the question of what level their visual cortex still functions, the breakdown of humours in the eyeball and degradation of the cornea will leave the zombie with very poor eyesight. It is doubtful whether zombies would be able to detect between the fresh glean of healthy skin and the dull, pallor of undead flesh, let alone subtle changes in posture and muscle condition, so on visual inspection alone a zombie could not discriminate between you and a zombie standing next to you. More easily detectable signals such as high contrast or sudden movement are probably within its' perceptual range. And to be safe, I am assuming they may still be able to detect characteristic purposeful human movement.
Less is known about zombies hearing. Again we can expect a fair degree of degradation in their perceptual abilities. Zombies not only lack language but do not seem to respond to even simple spoken commands or requests. Their own 'communication' is restricted to a low moaning or 'death-rattle'. They do retain the ability to localize sound sources and show some awareness of the special nature human vocalization. However, they appear to show no higher understanding of zombie-directed speech. Likewise, although there are no known dichotic listening studies with zombies, anecdotal evidence suggests they are easily confused by multiple sound sources. It is likely that respond aggressively on only a very primitive basis to the highly salient stimuli in the characteristic mid-range frequencies of normal human speech.
Although I know this is a controversial opinion, personally, I dismiss the possibility of zombies detecting humans using olfactory cues. Certainly, little is known about the working of the human olfactory system. It is conceivable that in the absence of higher cognitive function, this relatively independent mid-brain system may have stronger influence on behaviour, I feel the cues will not strong enough. From an evolutionary psychological perspective, I feel that our sense of smell is far more likely to be tuned to the avoidence of putrefaction and decay than the detection of fresh brains. It just smells wrong to me.
In my opinion, by the wearing of drab clothing, the simple avoidance of sudden, seeming purposeful movement, a lowered gaze and the restriction of vocalisations to the lower registers, you should be able to walk amongst the zombies relatively unmolested. Although it might be not necessary, a lower standard of person hygiene might help and may in any case be unavoidable. However, further research is required.