In general, low valued thick film resistors will be cleaner than higher valued ones. I'm using a Yageo 5025 case RC series thick film 100Ω part in a power supply location, but it does get signal current through it, so I gave it a bit of concern. The datasheet says that the excess noise is only 10dB for 100Ω and lower, whereas excess noise irises from 24dB to 46dB for values from 100Ω up to 1MΩ. This part was heavily filtered as well, so it seemed safe (and measures well enough). For thick film, excess noise and voltage coefficient are related, since they are both caused by the granular nature of the conducting material. Just like a carbon composition resistor, lower resistance values will have less noise and voltage coefficient.
So, if you can use a very low value, a thick film will probably be good enough.