I don’t have a whole lot of resources at my disposal and I’m on a phone, but the Native population is credited with exemplary and dedicated service to the US military. Bear in mind that the “Indian Wars” weren’t exactly faded from memory. The S-A War began in 1898. Massacres such as Wounded Knee (1890) and Little Bighorn (1876) were fresh in the minds of many, particularly the Natives. Speaking in relatives, it is the equivalent of the end of WWII and the end of the Korean War - not exactly ages ago. Many of the veterans from the Indian Wars were now becoming ranking military officials such as Nelson Miles, who would eventually become Commanding General. I mention this because it added to tensions on both sides.

Despite resentment from both sides, Native participation was strong and the military was receptive for a few reasons. First, being a warrior was ingrained into Native culture. It was almost expected to serve in a fighting capacity in the name of honour and pride. Second, many wanted adventure. Thirdly, joining the US military could potentially have socio-economic benefits, as well as potential earned respect, so many sought to improve social and economic standings. For the government, assimilation was key. This began in the early 1890s by recruiting nurses for $30/month and scouts with specialty military training- again for assimilation. Even Teddy Roosevelt was mostly unsympathetic towards the plight of the Native peoples. He is quoted as referring to Indians as “savages” on multiple occasions and praising pioneers for their “righteous” conquest. Still, he confessed that some white men were responsible for butchery and that certain Indian leaders deserved recognition as courageous and possessing integrity. Teddy would also rather see the Native tribes assimilate than to become extinct.

According to Jon Ault, who authored information for the S-A War Centennial:

Formally mustered on 30 April, two hundred Arizonans reported for duty at the regiment’s training grounds, Camp Wood in San Antonio, Texas. Other officers culled recruits for the unit from neighboring territories. 340 men came from the New Mexico Territory. Among them were two brothers, Joseph and Frank Brito of the Yaquí Tribe, who became privates in Troop H of the New Mexico contingent. From Indian Territory came 170 men, under the command of Allyn Capron, Jr. Among them were Thomas Isbell, of partial Cherokee descent, and William Pollock, a full-blooded Pawnee

That is at least 710. According to the US Census for 1890, there were 248k. So about 0.28% of all Indians for these regiments alone. During WWI, it is suggested that about 12,000 served according to the Naval History and Heritage Command. The 1910 Census shows that there were 291,018. That’s 4% of all Natives serving.

While you asked about participation since the Spanish-American War, I will also note that they have been documented serving during the War of 1812, the Civil War, etc. These numbers may seem low, but the recent history with the government and perhaps inadequate data might skew this. Hope this was what you’re looking for!

Sources:

https://www2.census.gov/library/publications/decennial/1910/volume-1/volume-1-p4.pdf http://www.spanamwar.com/NativeAmericans.htm https://www.history.navy.mil/research/library/online-reading-room/title-list-alphabetically/t/american-indians-us-military.html