Sooty mold grows on honeydew from aphids and other sweet juices. What you picture is not that. https://en.wikipedia.org/wiki/Sooty_mold  The photos are showing very old  stems.  The best  way to rejuvenate your shrubs would be to cut those old stems down to ground level and allow the newer, younger canes to flourish.  Yes, something has chewed a few holes in leaves but that is nothing to be concerned about.

Thank you for your response Barbara. I don’t think I posted adequate pictures. Can you look at these additional pictures and give me your thoughts? Thank you so much!!!

I still just see old canes that are splitting.  Viburnums are very hardy shrubs and the removal of those old canes will get good for the plant.  It also will give you some leaves at the  lower portion of your shrub.  I do some renewal pruning each year on mu viburnums to keep them full and vibrant.