I don't see why singing soviet anthem can make any trouble. (Well with Russian (/Ukrainian) police one can be in trouble without any reason but why with anthem specifically?) Yes, normally no one sings anthem if it is not official ceremony. Post-soviet people are cynic and singing anthem with no reason can make them giggling. But there is no specific prohibition of soviet symbolics AFAIK.

Well, in some public places loud singing can be treated as hooliganism no matter of what is singing exactly.