There are two schools of thought about pruning, or so it seems. If you watch the various YouTube videos. You’ll find that some garden experts will tell you to wait, depending on the plant. Without harsh electronic equipment you can prune carefully and discriminate from plant to plant, depending on the flowering pattern.
However, it is possible to prune and leave the new growth intact. Just use secateurs and prune to the next shoot, slowly. Not only will you be rewarded in a month or two, but you’ll keep the garden looking fresh and serene. I’ve done this with the Mexican Orange below; and the clematis.
You can trim the dead flowers off the Buddleia and thin to a third, to maintain the health. The best time is spring, although it is possible to do this with care in September.