Hello,

Your snowball viburnum blooms in the Spring, so it is best to prune it right after it flowers. Prune it any later, and you'll be cutting off next year's flowers. (Blooms on "old wood.") Here is an excellent link that talks about how to prune a snowball viburnum: http://www.gardenguides.com/80290-prune-snowball-viburnum.html and here is another, sourced from the "bible" of woodies, Michael Dirr: http://www.sustainable-gardening.com/plants/shrubs-and-trees/viburnum-macrocephalem-snowball-viburnu....

There are several ways  you can prune the whole shrub.  Dirr recommends pruning the whole thing back to 2-3 ft above ground in early Spring and have it grow back.  I would do that only if it were getting too tall or crowded (you can remove the excess stems as they grow back)..

Another way of renewal pruning is to take out the oldest canes, no more than 1/3 of the total, every year.  This is a good way to avoid a thicket of canes.

I found no information on pruning side branches to get a tree form, but one of the sources said you can prune anytime.  It may be, if you prune out the oldest 1/3, you won't have so much side-branching on the younger canes.  You can certainly top it off, which will give you a thicker, more branched, top.

It may be that you are just fighting Nature by trying to keep the stems bare.  Some plants just want to be the way they want to be.  This shrub, though, seems like it can take some experimentation because you can always cut it all down if you don't like what you did to it.

Best of luck.