Schmidt had two recorded boxing matches according to Box Rec;
http://boxrec.com/en/boxer/84149
First he won against a nobody.
The second is quite impressive, with a no decision (probably an exhibition) again Fireman Jim Flynn on Nov. 20, 1911. Flynn was one of the "great white hopes" that lost to Jack Johnson in both 1907 and 1912. That is probably where the Johnson/Schmidt story comes from.
Flynn fought all the big names of that era (both winning and losing). Even knocked out a young Jack Dempsey in the first round in 1917. So Schmidt even thinking of getting into the ring with him, is quite impressive.