It is documented in early U.S. Chief of Ordnance - 'Annual Reports' that the bayonet for the U.S. Krag was copied from the contemporary Swiss, Schmidt-Rubin, bayonet, (for use with the Swiss model 1889 rifle).

The blade of the later, Swiss model K-31 bayonet, had a different two edged - 'dagger' profile.
IMHO, the Swiss may have borrowed the K-31 blade profile from the British Pattern 1888 bayonet, for the Lee-Metford & Lee-Enfield.

The K-31 bayonet grip remained like the earlier Swiss models.

(As a point of interest, In the early 1900's, when the British adopted the Short Magazine Lee-Enfield, they initially had a short bayonet. This was the Pattern 1903. It retained the Pattern 1888 blade, but, had a new style of grip. Later, they adopted the longer Pattern 1907 bayonet, which was copied from the Japanese Arisaka bayonet).

Attached Photo (top-bottom): Krag, K-31, Lee-Metford Pattern 1888 bayonets.

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