I wouldn't be worrying about the 10% viscose, I'd be more concerned about the 60% cotton, especially if HWE is to be used. But I'm fairly new to this game - so don't take too much notice.
I did several cotton chairs recently using fibre shampoo. They were very light coloured beige, and came up fine, and I'm going back to do their carpets next week, so I must be doing something right.
They also had an off-white cotton fabric dressing room stool, which was really dirty. I couldn't get it clean with fibre shampoo, so I offered to HWE it, at the customers risk. I hit it with HD-X, agitated and HWE'd heavily. It worked out OK.