Oliver, once the needles are off you can see what needs to be done. I would prune to the shape you want and then wire. You can do it now or leave it until early spring before the buds break. It does need thinning, but I like the shape and if it was mine I don’t think I would do much wiring just the tertiary branches rather than structure.
It is an ideal time to wire and prune trees dropping their leaves/needles. You can now see what you do when all needles are cleaned out. Branches are flexible and pruning has an extra advantage right now.
Fall/autumn pruning produces growing hormones over the winter, adding more back budding and new growth than spring pruning. Spring pruning just gives more strength to bud already established, while fall pruning produces more buds.
The wiring will not take effect before the growing season but is a good work schedule to do it now when the tree is in your hands. There also are a lot of other things to do in spring. Wiring right after the leaves drops and the branches being flexible is best.
Nice tree. Look forward to see more of it after your work 🙂