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Seconding the recommendation for Lush shampoo/conditioner bars!
I also use Dr Bronners travel size soap that can be used as body wash or to do laundry in the sink.
Get the Matador leak proof dry-through cases for all the soap bars – they’re great!
My other recommendation for 2 weeks in a carry-on is to air out the clothes you wear each day (just lay them on the back of a chair).
It makes them much less likely to smell and able to be re-worn without washing.