Lymph node: Given the location midway along the anterior belly of the digastric muscle and the fact that it moves with swallowing, a small lymph node is a plausible explanation. The lack of tenderness and the small size also support this diagnosis.

Salivary gland stone (sialolithiasis): Although the size is small, a tiny stone in the submandibular gland could present as a firm papule, especially if it's located near the duct. The movement with swallowing could be related to the stone's location within the gland or duct.
Benign tumor (e.g., lipoma, fibroma): A small, firm, and non-tender papule could represent a benign tumor. These are common in the submandibular region and could be fixed to the muscle or other underlying tissues.
Cyst (e.g., thyroglossal duct cyst, branchial cleft cyst): Although less common in this specific location, a small cyst could present as a firm papule, especially if it's not significantly fluctuant or tender.

Metastatic lymph node: Even though the patient does not have a known primary malignancy, a metastatic lymph node from an occult cancer (e.g., oral, thyroid, or other head and neck cancers) could present similarly. This diagnosis is critical to rule out due to its significant implications for prognosis and treatment.
Infectious lymphadenitis: Although the lack of tenderness makes this less likely, an infectious process could still be present, especially if the patient is immunocompromised or has a chronic infection.

Neurofibroma: A small neurofibroma could present as a firm, non-tender papule, although this would be less common in the submandibular region compared to other locations.
Paraganglioma: These rare tumors can occur in the head and neck region, including the submandibular area, and might present as a small, firm mass.
Kimura disease: A rare, chronic inflammatory disorder that can cause lymphadenopathy and eosinophilia, potentially presenting with a firm papule in the submandibular region.