Yes, you may use unscented soap and shampoo while in Ihram. The prohibition of Ihram specifically targets applying perfume (teeb) — which refers to pleasant fragrances deliberately applied to the body or clothing. Basic hygiene and cleanliness are not only permitted but encouraged in Islam. Nabi (shallallahu alaihi wa sallam) prohibited the muhrim (person in Ihram) from wearing garments touched by saffron or wars (fragrant dyes), indicating the prohibition is about fragrance, not cleanliness.
Use products that are genuinely fragrance-free — not just 'unscented' (which may contain masking fragrances). Avoid: perfumed soaps, scented shampoos, fragrant body washes, cologne, aftershave, scented deodorants, perfumed lotions, and aromatic oils. You may use: fragrance-free soap, unscented shampoo, plain water, miswak (tooth stick), and fragrance-free sunscreen.
Some scholars distinguish between intentionally applying fragrance and incidentally encountering it. Walking past a perfume shop or smelling food is not a violation. If you accidentally apply something scented, wash it off immediately — scholars differ on whether this requires fidyah when done unintentionally. To be safe, prepare your toiletry bag before the trip with clearly labeled unscented products. Many shops in Mekkah sell Ihram-friendly hygiene products specifically for jamaah haji.