60% viscose should be ok to wet clean (just), using HWE. I presume its in pile form and not flat weave? Flat weave definately no problem, pile is where the issues start.
But to be honest its the 100% viscose's that demand respect really. I would wet test, if no visible difference is there after drying off, then away you go and wet clean it. It shouldnt be massively different on a 60% fabric, but could you possibly notice a small amount.
Your right dry cleaning wont do much, so you could use min moisture to do it. Spray a microsplitter on to terry towels and wipe it over (not soaking wet on the towel). This will give a better result than dry cleaning and you shouldnt make any difference on the fabric appearance.
You could even spray dry cleaning fluid on the fabric, then the damp method mentioned - to keep the absorption to a minimum.