Step 1: Recall the core of Behcet's disease. It is a multisystem vasculitic disorder hallmarked by a triple set of mucocutaneous and ocular lesions: mouth ulcers, genital ulcers and eye involvement.
Step 2: Check each option. Recurrent oral aphthae, genital ulcers and uveitis all belong to Behcet's and may be accompanied by skin lesions and a pathergy reaction.
Step 3: Spot the outlier. Pyoderma gangrenosum is linked to inflammatory bowel disease and arthritides rather than to Behcet's syndrome, so it does not belong here.
Step 4: The answer to this except-type question is pyoderma gangrenosum.
\[\boxed{\text{Pyoderma gangrenosum}}\]