If you are worried about harmonics, you should definitely avoid PWM. Rectangular waves are jam-packed with harmonics that extend as far as pin slew rates permit. Although low-pass filtering will get rid of the higher order stuff easily, the lower order stuff will be harder to remove without some serious filtering. You don't specify how much harmonic distortion you could live with or what frequency range and waveshapes you are trying to generate (10kHz makes me think that you are trying to make an audio waveform generator), but you're fighting a losing battle that is going to end up with you needing external active components anyway - so why not add a DAC?
I'm also going to guess that you don't want to write any code, so a quick Google shows that Adafruit offer a MCP4725 breakout board with a prewritten library and tutorial. The MCP4725 is a 12-bit DAC. Even though its INL leaves something to be desired, you'll be a good order of magnitude better off than even your best efforts with the onboard PWM.
As Leon Heller says, if you really want to generate high quality signals (and over a much broader frequency range) you could go for a DDS solution. Analog Devices do some nice ones with onboard SRAM for arbitrary waveform storage, so you simply set the chip up, tell it to go and you're done - no need for a constant datastream. This is probably beyond your requirements at this stage, however. There are also a bunch of cheap Chinese boards based on the AD9850 all over eBay which might be of interest.