Given that n = 600 and p = 0.65, we can calculate the standard deviation of the sample proportion using the formula:
\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}
Substitute the given values:
\sigma_{\hat{p}} = \sqrt{\frac{0.65 * 0.35}{600}}
\sigma_{\hat{p}} = \sqrt{\frac{0.2275}{600}}
\sigma_{\hat{p}} = \sqrt{0.00037917}
\sigma_{\hat{p}} \approx 0.019481
Therefore, the value of \sigma_{\hat{p}} rounded to the nearest ten-thousandth is \boxed{0.0195}.