Between 1918 and 1920, stamps in the post offices changed as the Ukrainian National Republic introduced the General Issue of 1918 and later in the year the Trident overprinted stamps. But the old Imperial cancellers remained in use. I know of only one distinctive new canceller - and that was introduced by the Polish during their occupation of Kamenets Podolsk in 1920. They produced a canceller with Polish spelling (KAMIENIEC) - this is illustrated in the Fischer Catalog Tom II and on this Blog - click on the Label at the end of this Post to link to the relevant page.
There is also a Kamenets canceller with Ukrainian spelling (KAMYANETS) but this is a Forgery. Though similar in style to Imperial Russian cancellers, it appears to have a fixed date 19. 7 19. It is only found on cancelled to order stamps, some genuine and some forged or doubtful. The ink used for all cancellations is different to the inks generally used in Podilia during 1918 - 20. Here are some examples of the cancellation. At the top it is applied to a genuine 20 Hr General Issue, a genuine type 3 Kharkiv Trident and a genuine type 1a Podilia Trident. Then at the bottom are two examples of Podilia 1a in violet or violet-black ink. These are usually regarded as Reprints or Forgeries though the discussion in the Trident literature is pretty perfunctory.