If that's what you want to do then go for it. Cutting back shrubs is a good way to rejuvenate old plants.
What is usually done is each year, and the time can be right after flowering, cut back the old shoots...the ones in the center.
Do not remove more than 25% each year...so that after four years of pruning, you have an entirely new plant.
Cut these old shoots right to the ground.
You can tell which are the oldest shoots by the color of the wood.

Viburnum snowball I remember having one in my backyard and the only problem we ever had with them was the earwigs were always around it.....possibly because the plant was situated near the outside tap and possibly the area there was moist from water leaking whenever the hose was used.
Because we were on a septic system at the time, the grass grew mightily and we used more snowballs as a hedge at the back of the property which bordered a farm.
I caught a cow once with her face in the plant....but she wasn't eating it...so I assume the flowers or the smell of them attracted her.