Nobody has asked how large this appliance the OP is wanting to build has got to be. Sure, while I agree with the comments about the safety and regulatory issues, it's easy to think a relay implies a breadbox sized containter, but there are smaller relays, some, in fact, the size of really small SMT components. Now, the power rating of his relay suggests he's using a rather large one, but maybe judgment would best be reserved until precise dimensional data becomes available.

BTW ... Wall-warts are nice. Wall-warts are generally safe. Wall-warts are, however, sometimes, and quite commonly, prone to thermal failure, which, while not a threat, is certainly an inconvenience.

RE