On a 16 MHz Arduino your choices for 8-bit (Phase Correct or Phase and Frequency Correct ) PWM are 31,250 Hz or 3,906.25 Hz (prescale of
. Neither is close to 10 kHz. You can adjust the frequency upward by using a value for TOP that is less than 255 but that cuts into your PWM resolution.
The hard part will be finding an integer value for TOP that produces a frequency near 10 kHz that is an integer multiple of 60 Hz. Your choices of TOP to get within 10% of 10 kHz are 91 through 101. None of them produces an exact multiple of 60 but a couple come close. The closest one is 101 -> 9900.990099 Hz -> 60*165.016 -> 165 * 60.0060006 Hz
If you have to have both 10 kHz +/- 10% and exactly 60 Hz you will probably need to use a non-standard system clock crystal. I think a 16.032 MHz crystal might work (if you can find one). Use a TOP of 100 to get 10.020 kHz and divide your sine wave into 167 samples to get exactly 60 Hz.