We present the results of a spectroscopic monitoring campaign of nine presumably single Wolf-Rayet (WR) stars, eight of type WC 9 and one WC 8d. We characterize their variability and search for clues to the mechanism responsible for the formation of dust in their wind. For seven out of eight WC 9s, we find a large-scale line-flux variability level of {sigma}>5-8 per cent. The only WC 8d star is variable at a level more comparable with those associated with wind clumping, {sigma}=2.2 per cent. The changes take place on a time-scale of days but in many cases, observing over longer time spans resulted in higher line-flux variability levels. The width of the substructures ranges from ~150 to 300km/s, with the widest structures corresponding to stars with the highest variability amplitude. We searched for periodicities in integrated line quantities for CIII {lambda}5696. Radial velocity changes are typically ~20km/s but never exceed 40km/s and are anticorrelated with the skewness of the line, strongly suggesting that they do not correspond to a real movement of the star. No periodicity was found in these integrated quantities, except for WR 103. Therefore, a wind-wind collision in a close binary does not seem to be responsible for the short-term variability. We cannot, however, exclude that these stars are intermediate- to long-period binaries. We estimate that for periods up to a few years, the shock-cone resulting from wind collisions would be non-adiabatic and thus unstable. We suggest that this represents a viable mechanism to explain the spectroscopic variability.