Will acrylics irritate the skin or cause any problems? I am using Acrylic White Plastic and wanting to cut it down into small pieces to use as...

You need to check further with the manufacturer to be sure. There are problems for some people with certain types of acrylic, but it sounds as if it usually happens when it is in powder form, or in situations in which it is held in contact with the body for long periods of time--specifically, acrylic fingernails. From what I can learn, some types of acrylics are more likely to cause reactions than others. If there is a manufacturer listed on the product you are using, you could try contacting them for acceptable uses for that type of acrylic.