When he was in the badlands in the 1880s there was plenty of opportunity for him to die either by accident or in fight. What are the later effects, especially on New York politics, federal politics, the US Navy & Spanish-American War?
The Maine could even not sail for Havanna. I have to research that though.
I'm sure, however, that without Roosevelt's direct order Dewey would not have sailed for East Asia, or at least not as soon as he did (which was something very irregular actually). There is a chance that if a Spanish-American War still happens, it's a more limited affair that takes place in Cuba only.
I discuss possible alternatives to TR as Republican vice presidential candidate (and future president, unless McKinley's assassination is butterflied away) at https://groups.google.com/d/msg/soc.history.what-if/mMhFKXMfSVU/-411NnI85KgJ Most of them seem more conservative than TR--indeed, some of them may be more conservative than McKinley...