How can we recreate old pharaos' perfumes?
The analysis won't be done before lunch, but neither will it be an extremely difficult process.  Certainly some of the researchers will have a fragrance industry background  and access to necessary equipment like  a tandem gas chromatograph - mass spectrometer.  Also, Pharoah's perfumes were undoubtedly less complex than todays, and all oils used in perfumes are available as "known" compounds for comparison.  Additionally, all fragrances have been "fingerprinted" making identification of the compound in a sample fairly routine and straightforward.  By "fingerprinted" I mean that if a certain pattern of compounds can be detected than they will suggest the presence of a certain oil.  For example, look at lavender oil, there are about 30 chemical components in it - just like a fingerprint.

Perhaps the base solvent has evaporated through the wall of the container and oxygen has flowed into the container.  Certainly some of the ingredients will have degraded, but the container won't be full of acetic acid.  Some amount of an alcohol may have oxidized to the corresponding ketone, aldehyde or carboxylic acid, perhaps some amount of a conjugated diene may have oxidized to the corresponding dienol; but that shouldn't make the process that much more difficult.