By chance, last night I did my first processing session using trays rather than drums, and I used Tetenal's RA-4 chemistry kit. It's certainly possible, but you've got to do it in a completely dark room (no safelight) or with a type of safelight that I don't have and that I've heard is very dim. Thus, you must know the way around your darkroom in the dark.
Personally, I didn't have any problems with my session -- at least, nothing major. The main problem was that the Tetenal blix had some small undissolved particles in it at first. I shook it up in a jug and that took care of most of the particles, but some still clung when I removed the prints from the blix tray. I had to wipe the prints with my hands in the wash to get it off (a squeegee would probably have worked, too). These particles slowly dissolved (or maybe were carried out on prints) over the course of my session. Also, the odor from the developer and blix gradually increased over time; my darkroom isn't yet as well ventillated as it should be.
Overall, I think I preferred this method to working with drums; I found it quicker to get on to the next print without having to wait for the washing to finish, much less dry the drum. (When I first started with color printing, I had problems with streaks from small drops of water that dripped at inopportune times with poorly-dried drums.) Maneuvering prints in and out of trays in total darkness isn't as hard as I'd feared it might be. Try practicing with B&W prints, if you like.
FWIW, the Tetenal instructions that came with my kit do address use in trays. If there's different packaging in Ukraine and such instructions are missing, post here and I'll summarize, or maybe scan the relevant pages for you.