I am no expert, but, looking at the 'grinding' marks, I think that these do not seem to be made by a file.
1. File teeth are triangular and equally spaced... ^^^^^^^......the grooves on your picture appear to be 'rounded' and not regulary spaced... n nn n n
2 The grooves seem to follow most of the contours of the surface, a file would only remove 'high spots' and the file teeth would not be in contact with the 'low spots' as the file is, in 'essence', flat.
Perhaps these 'marks' are caused by working the axehead on a 'grainy', soft(sedimentary type) rock
It is difficult to be precise with photographs, lighting etc can cause 'mis-leading images. Of cause, even if I am right, this would not guarantee 'authenticity' ... a 'good faker' could imitate this effect. Equally, though, you could say that it would add 'weight' to their authenticity
Perhaps the curator of the museum (you mentioned) could point you in the direction of someone whom could authenticate them properly for you.
If they do turn out to be genuine........
All the best