Final answer:
The skin condition described is most likely basal cell carcinoma, a common skin cancer caused by long-term sun exposure and characterized by a pearly or waxy bump that bleeds easily.
Step-by-step explanation:
The most likely diagnosis for a 50-year-old white man presenting with a small, flesh-colored papule with central ulceration that bleeds easily on palpation is basal cell carcinoma. Basal cell carcinoma typically occurs due to long-term sun exposure affecting the mitotically active stem cells in the stratum basale of the epidermis. This type of skin cancer commonly appears as a pearly or waxy bump on the skin and is the most common cancer in the United States. While it rarely undergoes metastasis, early treatment is crucial for the best outcome and may include surgery, cryosurgery, or topical ointments.