It wouldn't be correct since you would be thinking of a specific soap, rather than soap in general. Here the focus is on the fact that she uses soap, it could be different soaps at different times.
If the Norwegian sentence was "Hun vasker hendene med en såpe", then your translation would have been correct.
Answer to question: I think it is more to do with English than Norwegian here. Soap isn't a straight up noun. It is a material so more often used as an adjective to describe what something is made of.
Extra words-words for fun/further info: "...with a bar of soap." should be acceptable but "a soap" would only be used if you were then to describe a specific soap. eg "She washes her hands with a soap smelling of roses." This would then be moving emphasis from the act of washing hands with soap, more onto the significance of the soap.
Sooo, if someone was for example, a serial killer collecting hands as trophies, how would you say "She/He/They/I are washing the hands (that aren't theirs) with soap." ?
As in Norwegian the "their/her/his" is omitted in place of a simple "the" how do you distinguish the difference?
Hope someone can help me with this, it is kinda important for... reasons...
If I understand your question correctly, you want to know how you would write this sentence if you were washing someone elses cut off hands. If the hands belonged to a man it would be "Jeg vasker hans hender" or "Jeg vasker hendene hans" if I'm not entirely mistaken. Have I done a grave mistake in providing you with this information? ;)