It would be better to use a .457" lead ball with that Walker, or any Dragoon.
The big "horse pistols" for whatever reason tend to run with larger chambers than the 1860 Colt, 1858 Remington and other .44s.
Speer and Hornady make swaged .457 balls, available throughout North America in any well-stocked outdoor or gun store. Frankly, I wish they also made .462" balls. I learned many years ago, and have counseled for some 20 years, that oversized balls create wider bearing bands when they are seated in the chamber.
This wider bearing band provides more surface area for the rifling to grip and engrave, and keeps the ball from sliding forward during the recoil of other chambers being fired.
The larger bullet, by virtue of its wider bearing band, also seems to promote better accuracy. Certainly, it does no harm.
All of the Colts, including the originals made in the 19th century, shoot high at 25 yards. They were viewed as supplanting the rifle out to 50 or 100 yards. An exception is probably the .31 caliber pocket Colts. They still shoot high, but lose accuracy rapidly beyond 25 yards. But then, they were only intended for personal protection at across-the-table ranges.
Enjoy that Walker, but remember that if you have problems with it, at only 1,100 made it was essentially a large production prototype. Lessons were learned and improvements made that were instituted in the Dragoon models that followed. The final Dragoon, the 3rd Model, is in my estimation the best of all the old "horse pistols."