Cornstarch might not be the best choice... there are lower temperature starches, such as arrowroot, that will impart a softer texture that might be less slimy. I've used arrowroot in dairy-free ice cream and it sets just fine at low temperatures.
There are other low temperature starches, such as guar gum and xanthan gum, but both of these are a little more challenging to work because they can setup forming very stiff protein networks in the pudding and result in an unpleasant texture.
@spbeckman Great advice.