This sounds like a good candidate for the procedure you outline, done with loose fill cellulose insulation, with two caveats.
First of all, while this could conceivably be a DIY project, you can't rent a typical cellulose blower from Home Depot or the like because it doesn't have the power to really densely pack the stuff in there; as a result, the material will settle and you'll wind up with an uninsulated band on top. You need one of the more powerful professional machines that can do wet-blowing and dense-packing.
Secondly, you live in a rainy climate, and it's likely that the empty wall cavities have been permitting the boards of your wood lap siding to dry readily when they get wet due to convection within the wall and heat leaking out from the interior. These traits are bad from the perspective thermal comfort and utility bills, but fixing them will in all likelihood reduce your walls' drying potential, which could lead to your siding rotting and the paint peeling. If your house has very wide roof overhangs or a wraparound porch or something such that the walls rarely get very wet, this may be no big deal. But if not, the outlines project is much riskier and it may be worth it to expand the project and remove the siding so you can install modern sheathing with a weather-resistant barrier like double-layer tar paper or Tyvek. And if you're going to do that, you might as well add even more insulation in the form of several inches of rigid foam or mineral wool boards over the sheathing--or even in lieu of wood sheathing, in the case of foam!