The verb shed is uninflected in the past tense and as a past participle. For example, she shed some fur yesterday and she has shed her excess fur are correct, as is we found some shed skin on the ground. Shedded appears occasionally, but dictionaries don’t recognize it, and it is rare in edited writing.
Once inside she shed the coat to reveal a silver ruffled dress. [Daily Mail]
The unemployment rate has shed a full percentage point in the last four months. [CNN]
[T]he shed fur is swooped into the vacuum chamber. [Racked]