One of my favourite tea-scents is Serger Lutens’ Five O’clock Au Gingembre. Maybe you like it. There’s no sandalwood in it and no lime (but ginger and bergamot which adds an hesperidic edge). It’s definitely unisex and easy to wear, but also quite unique.
From the notes you might also like to try Sandalo e Thé by Bois 1920.