There is nothing magic about Y class capacitors---they are simply capacitors which have been verified to meet all the specifications of the "Y" classification.
Which includes that they have to fail open. Standard ceramic caps have both failure modes: open and short. I don't think that you would like the latter, especially when the front plate isn't grounded. Not just an unpleasant zap.
As it is a fixed cord,it would be simple to fit a 3 wire one.
Yup!