Is this an appropriate song for a tradcat to sing?  I find the tune very stirring.  I do not think I see anything against the Catholic faith in the lyrics.  I know the history of the song and that is not what I am talking about- is there anything wrong with the lyrics?

I don't know. Good rousing tune though.

Also, are there any traditional Catholic hymns of that nature- sort of inspiring battle-type hymns?

Faith Of Our Fathers comes to mind.

Faith of our fathers, living still
In spite of dungeon, fire and sword,
O how our hearts beat high with joy
Whene’er we hear that glorious word!
    Faith of our fathers! holy faith!
    We will be true to thee till death!
   
Our fathers, chained in prisons dark,
Were still in heart and conscience free;
How sweet would be their children’s fate,
If they, like them should die for thee:
    Faith of our fathers! holy faith!
    We will be true to thee till death!
   
Faith of our fathers, Mary's prayers
Shall win our country back to thee;
And through the truth that comes from God
England shall then indeed be free.
    Faith of our fathers! holy faith!
    We will be true to thee till death!
   
Faith of our fathers, we will love
Both friend and foe in all our strife,
And preach thee, too, as love knows how
By kindly words and virtuous life.
    Faith of our fathers! holy faith!
    We will be true to thee till death!


(The verse about England varies!)