Do angels sing?

Why would the living creatures (not angels) or the 24 elders sing and pro-claim they were redeemed by the blood?

They were not

8 Now when He had taken the scroll, the four living creatures and the twenty-four elders fell down before the Lamb, each having a harp, and golden bowls full of incense, which are the prayers of the saints. 9 And they sang a new song, saying:

“You are worthy to take the scroll, And to open its seals; For You were slain, And have redeemed us to God by Your blood Out of every tribe and tongue and people and nation,

I'm looking into this now as well. Actually this is the second time I've looked into this as far as what the bible says. I agree with what you've heard that the Bible doesn't unequivocally say that angels do sing. The closest verses I can find to say they do would be from Rev 15:2-3. From my understanding of this passage (which is pretty limited) its a reference to Rev 4:6 where there are angels in the back but 4 beings which represent the whole created order and possibly the 24 elders as well doing the singing, not the angels. Like you said, every other time they say or declare. Which could be taken as singing, but you can't know for sure. That would be the closest scripture I can find to coming close to saying Angels sing though. Maybe you could say that in Job 38 the stars singing are angels, but I don't believe that. That being said, I personally think angels can and do sing, I just don't have a bible verse to definitively say that.

Angelic beings do literally sing praises as depicted in scripture (ref Isaiah 6:2-4 and Rev 4:8; 5:8-10; 7:11-12).

Biblical scholars support this belief. For example some believe that Isaiah's vision of the angels included a antiphonal song, that is a song where small pieces are sung by alternating singers:

Isa. 6:3. “And one cried to the other, and said, Holy, holy, holy is Jehovah of hosts: filling the whole earth is His glory.” The meaning is not that they all lifted up their voice in concert at one and the same time (just as in Ps. 42:8 el is not used in this sense, viz., as equivalent to c’neged), but that there was a continuous and unbroken antiphonal song. One set commenced, and the others responded, either repeating the “Holy, holy, holy,” or following with “filling the whole earth is His glory.” (Keil and Delitzsch Commentary on the Old Testament, 7.124)

Music and singing has always been connected to worship, and worship always connected to the concept of heaven. Therefore Jewish, Christian and even folklore has held the tradition that angels sing. Medieval folklore even imagined that those on the top of the tower of babel could hear angels singing.

Considering the view of heaven which the book of revelation brings us to, it is not surprising that we find angels singing:

And when he had taken the scroll, the four living creatures and the twenty- four elders fell down before the Lamb, each holding a harp, and golden bowls full of incense, which are the prayers of the saints.

And they sang a new song, saying,

“ Worthy are you to take the scroll and to open its seals, for you were slain, and by your blood you ransomed people for God from every tribe and language and people and nation (Revelation 5:8-9, NIV)

The Greek word for sang means 'sang' it does not mean anything else, therefore we are to imagine these words literally being sung. The four living creatures are understood to be angels. Even if they were not it shows us the practice of those surrounding Christ in heaven. If the church worships God on earth, why would we not have worship services in heaven, along with angels.

Traditional commentaries always consider the angels visitation to the shepherds as words of singing. This is what various Christmas carols remind us of:

And suddenly there was with the angel a multitude of the heavenly host praising God and saying, “ Glory to God in the highest, and on earth peace among those with whom he is pleased!” (Luke 2:13-14, NIV)

Alfred Edresheim the Jewish historian gives very detailed information on Jewish angelology at the time of Christ in the synagogue, part of which covers singing. Although is many unbiblical things that were believed at the time, it still established the ancient traditional understanding:

The Ministering Angels and their Ministry. The ministry of the Angels may be divided into two parts, that of praising God, and that of executing His behests. In regard to the former, there are 694,000 myriads who daily praise the Name of God. From sunrise to sundown they say: Holy, holy, holy, and from sundown to sunrise: Blessed be the Glory of God from its place. In connection with this we may mention the beautiful allegory (Shem. R. 21) that the Angel of prayer weaves crowns for God out of the prayers of Israel. (Alfred Edersheim Life and Times of Jesus, Appendix on angelology)

Interesting they thought angels were like fire in their quickness to obey God and in their singing, like flames. This has biblical merit.

Of the angels he says, “He makes his angels winds, and his ministers a flame of fire.” (Hebrews 1:7, NIV)

Fire is both quick and pure but also often expresses passion which would be filled in their singing.