I didn't know what game this is for, so I answered for all games where aegislash is available. These games are X/Y, Omega Ruby/Alpha Sapphire, Sun/Moon, Ultra Sun/Ultra Moon, Sword/Shield, and finally Legends: Z - A.
As I can't get clips of my own of these games, I resorted to youtube, and finding moments in videos where an aegislash uses swords dance
X/Y
In this video we can see an aegislash use swords dance in at 1:16, and it stays in the sheild form
Omega Ruby/Alpha Sapphire
In this video we can see an aegislash use King's shield at 8:23, which, like swords dance, is a status move. As it switches into shield form, we know the same thing will happen for swords dance.
Sun/Moon
In this video, at about 2:20, we can see aegislash uses swords dance and stays in shield form.
Ultra Sun/Ultra Moon
In this video we can see aegislash use the status move substitute at 2:02, and swords dance is also a status move. It stays in shield form, confirming that if it were to use swords dance, it would also stay in shield form
Sword/Shield
In this video we can see aegislash use the status move kings shield at 5:35, and as I have said before, swords dance is also a status move. It switches into shield form, meaning that would also be the case for swords dance
Legends Z - A
In this we can see at about 15:51, aegislash does not change into blade form when it uses king's shield, it stays in shield form. This means we can conclude the same thing will happen for swords dance as they are both status moves.
From this information, we can conclude that if you were to use swords dance in any game, the aegislash would be in shield form.
