Correct option: Carcinoma of the penis.
Step 1: The lymphatic drainage of the penis is to the superficial and deep inguinal nodes. So penile carcinoma classically spreads first to the inguinal lymph nodes, producing the lymphadenopathy described here.
Step 2: Penile cancer is preceded by recognised precancerous lesions (Bowen disease, erythroplasia of Queyrat, leukoplakia), which fits the precancerous lesion in the stem.
Why the others are wrong: Testicular cancer drains to the para-aortic nodes, not inguinal nodes (unless scrotal skin is breached). Prostate cancer spreads to the obturator and internal iliac nodes. Bladder cancer spreads to pelvic (iliac) nodes. None of these primarily seed the inguinal group.
Ref: Bailey and Love, Short Practice of Surgery, 27th edition, 2018.