It does have combustion-in-an-oxygen-atmosphere issues.
Unless you are using enhanced breathing engines thats about all yoiu are going to get in terms of ceiling.
The operational ceiling of the U2/TR-1 aircraft was listed at 80,000 feet, however they routinely exceeded that level during operations as did the SR-71. Those are air-breathing engines that burned JP-7, which has some blended oxidizers, but not alot. The flash point was so high that you could drop a lit match into a bucket of it and the match would go out. I’ve seen that with my own eyes.
My whole point is that if the Global Hawk ceiling truly is only 60,000 feet, most SA-7-like antiaircraft missiles could reach it, assuming the guidance radar could see the target.