Dear RayK,
That's very good of you to offer to repair the statue in your RC Church.
and just when I need to confer with another artist!!
We all cooperate in God's little miracles without even knowing it

.
Since you asked, these are my suggestions.
First, sanding down all the peeling paint would be your first step. You'll probably have to do some plaster repair work before you can start painting. There is a product called "Vatican Casting Stone" that might be useful in painting on a really thin layer - or just make a slurry of plaster and carefully add on successive layers till it looks right. One thing that will help you is probably not to work more than 20 minutes at a time. Our poor minds tend to dull after that period of time when focusing on one thing. That time break will give you a new refreshing look when you return to your work and you'll be able to accomplish more with fewer errors.
If the face is done in acrylics, it might be a good idea to use the same medium on the Virgin's hands. I'd use an acrylic primer first, of course. And, a matte sealer or maybe a satin gloss at the end. Be careful and don't use a high gloss (unless that's what the whole statue is covered in) as it will make the hands stand out too much.
You might want to make some plaster chips to practice the color on. This way you can hold them up to the face color to get a good match.
I'd begin with a yellow ochre (about 80%), red (10%), and a touch of black. You can also add in some green to brown it up a little. Depending on the face colors, you probably will need about 5 to 7 shades. Use your main color and then darken it two shades with a smigen of black and lighten the main color with white and yellow ochre two shades. There is such a thing as acrylic glazing medium that can help you create more depth and tonal changes. Try and follow the painting method as done on the face so that it matches as closely as possible - i.e. if there is a lot of detail or very little detail, that will direct your project.
Usually a person's hands are a slightly darker color than the face. Keep that in mind when matching your colors to the face. Besides, it's the face that should draw your attention and making the hands more of a focus (or "brighter" color) will distract from the statue.
Lastly, pray first - ask our Heavenly Mother to help you. Meditate on her life and how she used her hands - to tenderly hold our Savior; to wipe His tears when He fell; to prepare His food; to dress Him; to hold His hand going to the market; to teach Him to walk and eat and play; to put Him to sleep at night; etc. She will lead you in the best way to proceed with your project - just ask.
I'll keep your project in my prayers.