Research in the lab of Dr. Joel Coats in the Department of Entomology at Iowa State University indicates that chemicals produced naturally by two plants, catnip and the osage orange (also known as hedgeapple) repel German cockroaches. Folklore includes numerous claims that catnip and osage orange are repellent to insects and spiders. Results presented at the American Chemical Society National Meeting in New Orleans, LA, August 22-26, show that when given a choice between a surface treated with these plant oils and an untreated surface, German cockroaches spent much more time on the untreated surface. Graduate research assistant Chris Peterson observed the responses of the cockroaches. He said that “the roaches will venture onto the treated surface, stop, turn around and walk off onto the untreated surface.”
However your cats will be too stoned to catch mice so you might trade one problem for another.
Purchase the plants, not seeds, you can find them at pet stores and nurseries. Catnip, like all herbs, needs lots of light. Put it in your brightest window or supplement it with fluorescent lights. Then water only when the top half inch of soil is dry.
The catnip plant does not repel the roaches but rather a substance in the oil repels roaches. So you could also rub some catnip oil along your doors and windows, but that could create a larger problem.