Can asbestos shingle siding be safely covered with traditional chicken-wire stucco application if window and door frames do not require alteration?

No problem with safety, but you potentially create a larger waste disposal problem eventually. I have covered with vinyl siding, but no reason you couldn't apply stucco. Drape the cement tile with a tyvek membrane before nailing the lath.

This older house is on a ranch, and, hopefully, it will continue to be used for another fifty years. Thanks for your input.

Good luck with the project. Hopefully most of the lath will nail cleanly. Tip: Pneumatic nailers tend to penetrate more cleanly and quickly than pounding with a hammer.