Are there any risks using a non-microwavable plastic plate in the microwave?
Yes, there are risks. Avoiding those risks is the entire point of the microwave-safe labeling.

When plastic is marked as microwave-safe (in the US), it means that the material has been tested and found not to release harmful chemicals when heated, by FDA guidelines. This is a stronger assertion than just that it doesn't melt. Something that's unsafe in the microwave may not show it visibly; it may leach chemicals without melting.

It's entirely possible that something not marked as microwave-safe may actually be safe, and just not be tested. But you have no way to know, and you should assume that anything unmarked could potentially be harmful.