None of the fragrances are essential (pun intended), other than for fragrance. You could start without the neroli oil - it is a variety of citrus oil anyway.
What is more problematic is the vinegar -- I would suggest that both from a scent point of view, as from a use point of view, vinegar is undesirable. If you substitute cosmetic alcohol (96%) for the vinegar, it should make a fine, although unrefined, after shave. Due to the 'low' percentage of alcohol in the final concoction, you may end up with an opaque, rather than a clear liquid. This is not a problem in use, but is cosmetically (the AS's cosmetics, not yours...) undesirable.
Commercial after shaves with this level of alcohol are filtered to get a clear formulation.