When I play Guzma & Hala, after I search my deck for a Stadium, do I have to shuffle first if I'm also going to search for Special Energy and a Tool?

You can skip the shuffling after the Stadium search as long as you clearly tell your opponent you're doing the second part of the card. So if you're doing both parts you first discard two cards from your hand, then search for any Stadium you're going to take, then search for the Tool and Special Energy, then shuffle your deck.

Relevant cards

SM12_193

SM12_229