Sven,
From the following timeline, Willie Dunn certainly seemed to have adequate time to layout the rather rudimentary 9-hole golf course that was first built at Van Cortlandt in the late spring of 1895.
From the New York World of April 7, 1895 our man Dunn is already in the states, having come on a recent steamer.
By the time of the May 5th, 1895 New York Sun report it appears that "two estimates" have been already garnered by the group of rich guys who seem to want to have the public land for themselves, not necessarily for the general public and who are petitioning the Park Commission. Is it possible that one estimate was from Willie Dunn and another from Samuel Tucker?
As of this May 11th NY Press report, still no action is taken as the contractor's estimates haven't been received. At the bottom of the article however we see the respective experience with golf of the men involved.
Here again is the May 19th NY Sun report once approval was received.
Here again is the June 8th report once some limited play is begun on the new course. It states that the work began May 20th.
Whether Willie Dunn or Samuel Tucker, or both were involved, this report from November 26, 1896 details the original course.
From most accounts, Willie Dunn seems to have been quite an aggressive self-promoter. This article from the Mount Vernon NY newspaper "Daily Argus" from April 18th 1903 contains a number of exaggerations and questionable claims. Unfortunately, I've been unable to find page 4 yet, which may detail more of his "half a thousand" US courses to date.