Urinary Tract Infection (UTI) with Contamination: The presence of moderate squamous epithelial cells suggests contamination, which is common in women due to the proximity of the urethra to the anus. The mild dysuria and frequency, along with the small amount of blood (RBC 4-10), could still be consistent with a UTI, especially if the contamination is masking the presence of leukocytes or nitrate.

Dehydration or Concentrated Urine: The symptoms of mild dysuria and frequency could be exacerbated by concentrated urine, which might also cause mild hematuria. The absence of leukocytes or nitrate reduces the likelihood of a bacterial infection, making this a plausible explanation.
Urethral Syndrome: This condition, often related to urethral irritation or inflammation without a clear infectious cause, could explain the dysuria and frequency. The hematuria could be a result of the urethral irritation.
Hormonal Changes: Postmenopausal women can experience urinary symptoms due to hormonal changes, including dysuria and frequency, possibly with some degree of hematuria due to urethral or vaginal atrophy.

Bladder or Renal Cancer: Although less likely given the mild and intermittent nature of the symptoms, any degree of hematuria warrants consideration of malignancy, especially in an older adult. The absence of other findings does not rule out cancer.
Kidney Stones: While the symptoms are mild, kidney stones can cause intermittent dysuria, frequency, and hematuria. The absence of severe pain or other symptoms does not exclude this diagnosis.
Interstitial Cystitis: This condition can cause chronic pain, dysuria, and frequency, and sometimes hematuria. It's less common but should be considered if other diagnoses are ruled out.

Tuberculosis (TB) of the Urinary Tract: Although rare, TB can cause chronic urinary symptoms, including dysuria, frequency, and hematuria. The absence of systemic symptoms or a known exposure history does not rule out this diagnosis.
Sickle Cell Trait or Disease: In individuals with sickle cell trait or disease, hematuria can occur due to sickling in the renal medulla. This would be an unusual presentation but should be considered in the appropriate demographic context.
Benign Prostatic Hyperplasia (BPH) or Prostate Cancer in Females with Skene's Gland Issues: While BPH and prostate cancer are male conditions, issues with the Skene's glands in females can mimic some urinary symptoms seen in these conditions, including dysuria and hematuria, though this is exceedingly rare.