I planted this Red Osier Dogwood--Cornus sericea--mostly for the red wood in winter. And it's blooming for the first time, so I'm pleased about that as well.

However I understand that the red wood comes from newer growth and that I should prune the old wood. But the thickest central trunk-like branch--seen in the photo below--is carrying most of the blooms and secondary branches. Would it survive my cutting to the lowest branch? Would it be OK to wait until the blooms finish or do I need to do it now? Here's a photo: