Idiopathic edema: This condition is characterized by swelling of the hands (or feet) without an identifiable cause, which could fit the given scenario where no trauma, increased uric acid, or arthritis is present. It's a diagnosis of exclusion but often considered when other causes are ruled out.

Infection (cellulitis): Although the question does not specify signs of infection, cellulitis could cause hand swelling and should be considered, especially if there's redness, warmth, or fever.
Lymphedema: This condition involves the abnormal collection of protein-rich fluid in the interstitial tissue, leading to swelling. It could be primary (idiopathic) or secondary to another condition.
Venous insufficiency: Swelling in the hands could be due to venous insufficiency, although this is more common in the legs. It could be considered if there's a history of deep vein thrombosis or other venous issues.

Compartment syndrome: Although typically associated with trauma, compartment syndrome can occur without obvious trauma, especially in the context of reperfusion injury or certain medical conditions. It's a medical emergency that requires prompt intervention.
Nephrotic syndrome: This condition, characterized by significant proteinuria, hypoalbuminemia, and edema, could cause hand swelling. It's crucial to diagnose due to its implications for renal function and the need for specific treatment.
Heart failure: Right-sided heart failure can lead to peripheral edema, including swelling of the hands. It's a critical diagnosis not to miss due to its implications for cardiac function and the need for appropriate management.

Sarcoidosis: This systemic granulomatous disease can cause swelling in various parts of the body, including the hands, although it's less common.
Amyloidosis: The deposition of amyloid proteins in tissues can lead to swelling and other systemic symptoms. It's a rare condition but should be considered in the differential diagnosis of unexplained swelling.
Thyroid disorders: Both hypothyroidism and hyperthyroidism can cause swelling, although it's more commonly associated with other systemic symptoms.