Pruning flowering shrubs, if needed, is generally done right after flowering. Here’s a fairly in-depth set of slides from a class for Master Gardener Volunteers about pruning.
So, that’s the easy answer. A common followup question is about how much to remove. That depends on your space and reason for pruning. Both of these shrubs, nine-bark and mock orange, can occasionally be pruned nearly to the ground as a rejuvenation strategy. My nine-bark is a huge dark purple one and after years it was congested and I considered removing it. I chopped it all the way down in late spring and as it regrew I decided I really do like it. The open vase shape was restored. Now I go in each summer with long handled loppers and cut down the biggest, oldest stems. This way there are always a few stems with pretty shredded bark in winter, and a few vigorous stems with particularly large leaves, and plenty of flowers with the following pretty seed heads.
My mock orange is really in a too-small spot. I cut it way back each summer after blooming. It responds with long, new whips of foliage I can tie back to my fence, and blooms heavily the next summer. It is doing well after many years of this treatment.
Does this help? These shrubs are tough and happy in our climate. I hope you’ll prune away and be confident that if you screw up, just wait a year and try it a different way. Send photos if you need more encouragement/advice.

Pruning now means no spring flowers. If you want to prune soon, wait for leaves to yellow, as energy from them supports roots. You’ll get a strong spring & summer regrowth.