No, sorry to say pruning back a hydrangea under a fir tree will not make it grow into a lush shrub. The plant struggles due to root competition, dry soil and lack of sunlight. Best to move it away from the competing tree roots or place it into a large container that you water often. Hydrangeas are not heavy feeders and do great with just a spring application of compost or slow release plant food but they do need moist soil. Removing the old dead wood is a good way to clean up the shrub and pruning back long branches will stimulate growth but I suggest a three inch layer of compost over the roots in the spring plus more water in the summer. Soak the soil at least once a week around the roots and you should see improved growth. If the plant is offering few flowers the reason is most likely too much shade. Good luck and report back this summer so we can all see how it is doing. Keep growing, Marianne Binetti