Yes, you can touch a pea puffer. Some novice fishkeepers are undecided about touching a pea puffer because the fish is poisonous. However, while a pea puffer is indeed poisonous, its toxin is contained in its internal organs, so you’d have to ingest the fish for it to poison you.
Furthermore, a pea puffer’s toxin potency highly depends on its diet and environment. Wild pea puffers are said to be more poisonous than captive-raised ones. This is because the captive-raised fish have almost no contact with toxic food sources, bacteria, and algae that can affect their TTX levels.
Touching a pea puffer is safe, especially one that’s captive-raised.