The most conventional approach in old construction is to add cellulose insulation. this requires 1-inch holes drilled top and bottom from the outside through the siding. Insulation is blown in, or filled through the bottom hole, and topped off from the top hole. This fills any fire stop that might be installed. You will never remove and reinstall the same siding on a house this old, but you can install the plugs and use filler and paint to eliminate any evidence of your insulation job.
Check into blown in cellulose insulation, either DIY or by a reputable contractor. Your alternative might be to remove interior plaster walls and add insulation. This is a major project and would probably result in the use of drywall as a replacement. The advantage is it allows you to update insulation, electrical and plumbing all at once.