When using Mimikyu's "Impersonation" attack, can I discard a Supporter like Green's Exploration or Morgan and bypass the requirement that says you can only play the Supporter if you do such-and-such?

You can discard those types of Supporter cards with Impersonation, but if you don't meet the Supporter card's requirements you cannot do what is says.

Relevant cards

SM12_245

SM12_96