The answer to whether the .577 cal bullets will fit probably depends on the gun you own.
Some of the cheaper Italian rifled muskets have bores that can be different than the original .580 size it should be.
If the bore is truly a .580 like it is supposed to be, the .577 diameter bullets might be more accurate than the .575 dia bullet's you mention.
Many have found that for a rifled musket to shoot accuretly, the bullet should be about .002 smaller than the bore. The .577 would be .003 smaller which is better than the .005 smaller, .575 diameter bullets.
As for safety, both bullets are totally safe as long as you keep the powder load reasonably close to the 60-65 grain load that was originally used in the original guns.
As for the .575 diameter bullets you mention, these were intended for battle field conditions where stopping to wipe the bore to facilitate loading was not practical.
The thought was, make it easy to load in a fouled bore. Accuracy comes second in importance.
I say, give the .577's a try. You may be surprised at how well they shoot.