Non floral, preferably not sweet

How about Frederic Malle's Musc Ravageur Oil ? Note are bergamot, tangerine, cinnamon, vanilla, musk and amber - taken from theperfumedcourt.com.
Regina Harris Vanilla Amber oil ?

May we ask why non-alcohol?

Alcohol is in general the base for the vast majority of perfumery. That being said, there are a number of fragrance lines where there are some oil alternatives. I've enjoyed the oils I've bought from Ayala Moriel - Ayalitta is a fresh, green favorite of mine from her line.

Since she is looking for oils, lines worth exploring might be: dragonflyblue.com, Madini, Attar Bazaar, Auric Blends, Kuumba Made, and Nemat. That said, I am not sure if any of these are avaiable where you are. They all have lovely wood, incense or musk scents.

CB I Hate Perfume. His perfumes are oil or water based (most are available in both formats) and plenty of them are non-floral.

If oil based isn't mandatory, Parfumerie Generale also has a lot of non-floral perfumes.

To get more specific, the following are no- or low-floral and not too sweet, but most of them are alcohol-based:

Art of Shaving Sandalwood (Yes, it's a man's scent. I don't care.)
Bois 1920 Sushi Imperiale
Chanel Cuir de Russie (Well, there's iris. Does she consider iris to be floral? Since the iris note in perfumes comes from a root, one that doesn't smell the least bit like a flower to me, I generally don't.)
Comme des Garcons: Leaves: Tea
Hermessence Vetiver Tonka
L'Artisan Dzing!
L'Artisan Dzongkha!
L'Artisan Fou d'Absinthe
L'Artisan Navegar
L'Artisan Tea for Two (fairly sweet, but I think it's worth a try)
Le Labo Patchouli 24
Pacifica Tuscan Blood Orange (might be too sweet)
Parfumerie Generale Bois Blond
Parfumerie Generale Cuir d'Iris (again, unless iris root is a floral for her)
Parfumerie Generale Felanilla
Parfumerie Generale Harmatan Noir
Parfumerie Generale Iris Taizo/Oriental (unless...)
Parfumerie Generale L'Eau Rare Matale
Parfumerie Generale Cedre Sandaraque
Parfumerie Generale Un Crime Exotique
Robert Piguet Bandit
Serge Lutens Fille en Aiguilles
Serge Lutens Fumerie Turque
Serge Lutens Iris Silver Mist (unless...)
Serge Lutens Muscs Koublai Khan (might be too sweet, might be too sweaty.)
Serge Lutens Santal Blanc
Serge Lutens Serge Noire

ChickenFreak

Does Liz Zorn use an oil base? I know she does natural scents.

There are lots of oils in bath shops and boutiques, many non-florals. Take a look at the Davies Gate line. Their Mandarin is a nice orange. Not sure if Hermes still makes Eau des Merveilles body oil, but it's wonderful and completely non-floral -- citrus, woods, pepper, ambergris.

Not sure I understand this: ALL the frags you listed are water and alcohol based, not just Feminite du Bois. Do you mean to say that it smells of alcohol? That usually dissipates quickly.
There are many oils available, but if you want non sweet and non floral, you might want to look at musk oils. Most do contain some floral essences, because without them, the musk would be horrid, but they are not prominent. I really like Kiehl's Musk oil for that reason.