Final answer:
The most likely diagnosis for the 69-year-old man is chronic lymphocytic leukemia (CLL).
Step-by-step explanation:
The most likely diagnosis for the 69-year-old man based on the clinical history and test results is chronic lymphocytic leukemia (CLL). The presence of smudge cells and fragile B cells on the peripheral smear are indicative of CLL. Additionally, the patient's symptoms of rectal itching and burning pain, along with a persistent cold, can also be attributed to CLL. CLL is a type of cancer that affects the lymphocytes, which are a type of white blood cell.