Contact Dermatitis: This is a common condition that can cause redness and swelling on the hands, particularly on the thumb, due to exposure to irritants or allergens. The absence of injury, localized joint pain, and elevated WBC count supports this diagnosis.

Eczema (Atopic Dermatitis): A chronic skin condition that can cause redness, swelling, and itching on the hands, including the thumb. It's a common condition and fits the symptoms described.
Psoriasis: An autoimmune condition that can cause red, scaly patches on the skin, including the hands. While it can cause joint pain, the absence of localized joint pain in this case doesn't rule it out entirely.
Insect Bite or Sting: Could cause localized redness and swelling, particularly if the reaction is severe. The thumb is a common site for insect bites.

Cellulitis: A bacterial skin infection that can cause redness, swelling, and warmth. Although the WBC count is not elevated, cellulitis can sometimes present without significant systemic signs of infection. It's crucial to consider this diagnosis due to its potential for serious complications if not treated promptly.
Deep Vein Thrombosis (DVT): While less common in the hand, DVT can cause swelling and redness. Given the potential severity of DVT, including pulmonary embolism, it's essential to consider this diagnosis, even though it might seem less likely.

Sarcoidosis: A condition that can cause skin lesions, including on the hands, but it's much rarer and typically associated with other systemic symptoms.
Kawasaki Disease: An acute febrile illness that can cause hand swelling and redness, but it's rare and usually presents with fever, rash, and other specific criteria.
Erythromelalgia: A disorder that causes burning pain, heat, and redness in the hands and feet. It's a rare condition and might not perfectly match the described symptoms but could be considered in a differential diagnosis for hand redness and swelling.