I've never seen aphids on that old Spruce. So probably doesn't warrant spraying unless damage becomes severe. Five years ago we cut down and burned an old Lombardy poplar that was loaded with galls. Unlike the spruce, these galls were round. We opened one and it teemed with tiny green bugs, smaller than aphids (perhaps young). Yuk! Thank you Michael.
They suck the young tender spruce shoots which thicken and grow around them, eventually turn brown and dead.
By irritating the bark it forms a gall in which they lay their eggs. You seem to have a nice crop of them, they can do some pretty unsightly damage to your tree. You want my opinion, I would get rid of them right away.
The dead brown galls at this time of year don't have any of the insects left in them; the time to remove them is the fresh new galls in late spring or early summer, when the insects are still inside them. Though trimming all the galls off a large spruce isn't very feasible! - as the damage is not very serious, I wouldn't bother.
Spraying is really the only control for these, pruning them out does just as much damage as the pest does. They can do severe damage to the look of your tree, making it deformed and stunting growth on the infected areas, generally get worse every year. Quite often the needles will die back for some distance behind the gall. They won't seriously effect the health of the tree, but surely are not beneficial. For timing and control practices you need to talk to someone local who deals with these professionally. Internet sites and University extensions are pretty much useless for this, they are written from all different States or Countries. Although you can learn the life cycle and controls, timing is totally local.