The Spanish American War was started and finished in 1898.  Although there were probably many Model 1898 rifles issued during the war, there was also a significant number of Model 1895 and 1896 models used and even a few 1894's.  Most of the volunteer regiments were still using trapdoor Springfields from the 1870's and '80's.  Your 1898 was made after the war so if your relative was in the war in 1898, he couldn't have used that rifle or the pistol that you mentioned.

It might be fun to find out which specific regiment he served in and then try to learn the history of the unit and what weapons they carried.