Agree with TN Shooter, even an early New Service should handle light to moderate smokeless loads.
Disagree with Sunray, when the New Service came out in 1898, Colt advertised it for black powder ammunition.
I shot some 777 in .44 Special and .44-40. It shot well, but heated the gun up fast, and left it sooty. The light fouling cleaned up with tap water as advertised; then dry and oil.
Load 777 to fill the case to the base of the bullet, no airspace, but not compressed as you would with real black powder. However many grains that takes, that is your load.
Hodgdon says: "Testing has shown that Triple Seven will perform best when the bullet just touches the powder. Allow no airspace between the base of the bullet and the powder."
They also warn against using it for loads they have not tested. Whee!
A 1914 New Service is really a pretty modern gun, as such things go. The US military used the 1909 New Service .45 with smokeless ammunition while the automatic pistol trials leading up to the 1911 were going on. I don't think you will be doing it a favor by loading 777. Ken Waters' Pet Loads for the .455 Colt - Eley in the .88" Mk I case START at 5.5 gr Unique and a 250 gr Remington hollowbase with velocity in the low 600s. Even if you are using Fiocchi Mk II brass in the .76" length, I doubt you are pushing the gun. But, as Jeff Cooper said, you will do as you think best.