On my opinion, the main criterion for a reference is that it must be AVAILABLE. Either on Internet or in most university libraries. An unpublished thesis in Ukrainian which is not available on Internet does not satisfy this criterion. Such a reference is meaningless.
So the real options are: a) to leave the proof to the reader or b) to include it. I do not understand why you call the second option "not very good". What's wrong with including a trivial lemma? A reader for whom it is trivial will just skip the proof.
PS. Why don't you scan your thesis and put in on Internet? Even in Ukrainian.