Homes constructed in the early 1900s generally do not have insulated walls. This can be corrected during re-siding by installing rigid foam insulation under the siding. In your case, that would then be covered by an infiltration barrier (felt) and metal lath before putting on the new stucco. This will produce an insulated and stable wall for your siding, but will increase your costs compared to skim-coating. The window and door trim and other details will also require adjustment to account for the increased depth.
Since you are applying new siding, the most economical approach is to spray in cellulose insulation. Holes at the top and bottom of each story are drilled and insulation is first bottom filled then topped off. Balloon framing may cause increased material use as insulation will fill between the floors in some cases.