Either is acceptable. They vary by region, but another way to say the same thing is "it's too bad that...." It's generally true that "pity" is more common among British speakers. None of them would carry the literal meaning of shame or guilt to a native speaker when used as a phrase in the way you described.

You can say either, and the meaning is exactly the same. 1. I heard somewhere that 'pity' is outdated or only British word. Is it right? No, that's not true. 'It's a pity' is not at all outdated - we use this expression all the time in modern English. And it's not 'only' a British word. It is also used elsewhere. 2. If I say 'it's a shame', wouldn't such sentence have the shade of main definition of the word 'shame' and hurt feelings of the person I talk to? No, not at all. For English speakers today, there is no connection in our minds between the sense of shame, and the set phrase 'It's a shame'.