Changing the sliders updates those values (ui_char_color_red, ui_char_color_blue, etc.) in REAL time. They can be modified at literally any point in the match.. intermission, round starting, during the round, etc. You can even play as a multi-life class, change the slider, then die and you will respawn with the new color on your second life. The slider is directly tied to the value. You can adjust the slider, type ui_char_color_red in the console, and immediately see that the new value is in there.
So I guess I don't really understand how a console command would be a problem considering the sliders already set these values instantly and unconditionally. It would just be a quality of life change. Unless what you're saying is that adjusting these values in the main menu (while not connected to a server) is where the issue lies. But I'm pretty sure those get reset/defaulted when you join a server anyways.