Yes, the cortisone cream could get onto Puffin's body. Cortisone has a lot of side effects! Topical effects would include weakening the skin collagen and easy bruising. If Puffin gets it into his eyes, it might cause glaucoma. If Puffin preens himself and gets it into his system, physiological effects would include fluid and electrolyte imbalances (sodium retention and associated fluid retention, potassium loss) and immunosupression. Repeated ingestion over any time period longer than a couple of days would lead to inhibition of corticotrophin releasing hormone and therefore inhibition of ACTH secretion, which would be dangerous when the cortisone is suddenly stopped, resulting in an acute adrenal insufficiency crisis.
WASH HANDS before handling Puffin, Puffin's food and water, and Puffin's food and water bowls!