Re: usage of wipe
waflob has already suggested the answer: "Go and wash your face or hands and dry them with a towel"
Actually, the whole sentence sounds unnatural to me. I'd say, "Go and wash your hands and faces". I would not bother to add 'and dry' - I'd take it as evident that that was implied. I would also use 'and faces', not 'or faces', because it's unlikely that I'd give them a choice.
I'd also use the plural form 'faces', because that is natural in English - we think that, as there is more than one person, more than one face is involved.
Context is always important; labelling is rarely important.