I apologize for this delayed reply to your gardening question and hope it is still helpful to you.
Cutting back the dead material will keep the bush fresh looking and attractive so I would go ahead and do it if you can. The more new growth comes in the more difficult it will be to trim out old dead growth.
I would also remove the dead growth from the hydrangeas for the same reason.
Thanks for the question. Best wishes for a wonderful gardening season. Please stop in again soon!
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