That blackface minstrelsy had some influence some influence on border morris is beyond doubt. The words in the final part of the Broseley Morris Tune collected by E. C. Cawte from Annie Lloyd make this clear(Cawte, The morris dance in Herefordshire, Shropshire and Worcestershire, p. 201):

There was a little nigger, and he grew no bigger so they put him in the Wild West Show.
He tumbled through the window and he broke his little finger,
And he couldn't play the old banjo.

The oral testimony from original border morris dancers collected by Gordon Ashman and published in his article Custom in Conflict confirms the influence of minstrelsy. The only question is how big an influence it was.