Matsui's RC inks says it is good for applications on fabric and well as paper products. Paper doesn't get washed, but my concern wash when it gets wet during shipping, if the waterbased ink will run or smudge.Waterbased paper printing inks are fine for cardboard. They air dry, and with paper there isn't really a difference between drying and curing since it doesn't get washed.
Fabric printing ink will work too. I've done a few test prints that way for record keeping without problems.