Welcome to the forum. I like your moniker!
If the branches have been dead a long time then I don't think you have much to worry about. I have used insect damaged hardwoods, hickory, oak, maple etc. Once the tree or limb dies the borers move on to a live host.
If the limbs haven't been dead long and you are concerned, you can also place the stick in a plastic bag and fumigate with an insecticide, seal the bag and put out in the sun for a couple weeks. Between the insecticide and heat in the bag your insects should be toast. I did this to a couple sticks I suspected were harboring carpenter ants.
If the branches have been dead a long time then I don't think you have much to worry about. I have used insect damaged hardwoods, hickory, oak, maple etc. Once the tree or limb dies the borers move on to a live host.
If the limbs haven't been dead long and you are concerned, you can also place the stick in a plastic bag and fumigate with an insecticide, seal the bag and put out in the sun for a couple weeks. Between the insecticide and heat in the bag your insects should be toast. I did this to a couple sticks I suspected were harboring carpenter ants.