Are the hands rigid or designed to move? i.e like gloves. If they are rigid, you should be o.k painting them if you use water based acrylic paint. Don't use cellulose based paints as they will almost certainly adversely affect the latex. If using acrylics, you will need to wash the hands in detergent or washing up liquid to remove any oil or releasing agent, and let them dry thoroughly before painting. I would strongly suggest applying paint to a small, inconspicuous area and seeing how it goes before covering the whole thing in paint.
I don't know if this would work if the hands are designed to move, as you may have a problem with the paint cracking and flaking off. I can't comment on whether dye would be effective as I've never tried it.
If they're like a Latex mask, you should be o.k using acrylic paint. I have touched up a few cheap masks using acrylics to make them more realistic looking and never had any problems.
I think the secret is not to apply the paint too thickly.
There is a technique called "drybrushing" which could be useful, particularly if the hands have a surface texture. If you are not famiiar with the technique, it involves applying the paint to the brush in the normal way, most of the paint is then wiped off so only the barest amount of pigment remains and the brush is virtually dry (hence the term "drybrushing"). the brush is then flicked rapidly across the surface to be painted. you will find that the paint will adhere to, and enhance, the surface texture. any darker colour remaining below any raised surface detail will add depth and shading. It may take a little practice to get it just right, but it's a worthwhile technique to learn for lots of applications, (Corpsification for instance). The important thing is to have the brush virtually dry of paint. several very light applications are much better than one with too much paint on the brush.
Anyway, if you're chasing people around in the gloom with a mask and a big pair of latex hands, I doubt if any of them will stick around long enough to make sure that you are a nice, uniform colour all over...LOL!
Give it a go and let me know how you get on..