Could I play Blaine's Quiz Show and put down Munchlax which has no attack?
No. You can only choose to put down a Pokemon that has an attack you can declare to your opponent.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)

Relevant cards

Note: All applicable cards may not be listed below.
SM11_186
SM11_186