I'm not sure access to soap would actually be difficult. Lye soap, for instance, is ridiculously easy to make - it's lye (which is obtained by leaching ashes containing potash...hmm, where have I heard of that one before?), animal or plant fat (tallow, lard, or something similar to palm oil), and water. That's it.
It's not hard to make, and was commonly produced in house in frontier areas.
Before there was lye soap, it's known that the Greeks and Romans used Olive Oil as a type of cleanser. You'd massage it on, and squeegie it (I'm not even joking) off with a scraper. The oil would carry impurities with it. They also made great use of Rosemary, which has antibiotic properties.
So even without widespread availability of soap, most likely cooking oils are available and could be used in such a fashion.
It's not hard to make, and was commonly produced in house in frontier areas.
Before there was lye soap, it's known that the Greeks and Romans used Olive Oil as a type of cleanser. You'd massage it on, and squeegie it (I'm not even joking) off with a scraper. The oil would carry impurities with it. They also made great use of Rosemary, which has antibiotic properties.
So even without widespread availability of soap, most likely cooking oils are available and could be used in such a fashion.