The Time Mercenaries by Philip E. High (first published 1968)
Why it matches:
- Protagonist: A 20th‑century military airman (from WWII) is brought forward into the future and “upgraded” to serve as a commando. High’s text specifically mentions physiological enhancements, including greatly increased strength and a blood/oxygenation modification that lets him hold his breath for extended periods—exactly the ability later used underwater.
- Mission: He’s placed with a special-ops team sent by spaceship to the invaders’ homeworld carrying a nuclear device intended to destroy the planet and end the threat to Earth.
- The alien planet: It has two intelligent species. The land-dwelling civilization (the aggressors against Earth) is being squeezed by worsening climate/desertification and has begun building underwater cities to encroach upon the oceans, leading to war with the planet’s native marine species.
- Capture/escape: The team is captured on arrival and taken to an underwater city. The protagonist escapes and, thanks to his breath-holding enhancement, makes contact with the ocean-dwellers, ultimately aiding them against the land-dwellers.
- “Princess” and telescope detail: There is an interrogation scene with a high-status, alluring female from the land-dwellers; one memorable science-y flourish in the book is the use of a liquid-mirror telescope (a rotating pool of mercury forming a parabolic mirror) to locate/identify the visitors’ origin—an unusual but real-world technique that sticks in readers’ minds.
- Ending: Rather than blow the planet apart, the Earthmen realize that detonating the nuke in a suitable canyon/chasm could impart a net “kick,” shifting the planet outward to a cooler orbit and removing the climatic driver behind the invasion plan—precisely the skeptical-but-pulpy orbital-fix you remember.
Notes:
- In some summaries you’ll see that the airman is time-snatched rather than literally frozen in ice; that “Buck Rogers” feel can blur in memory, but the rest of the plot points line up closely.
- It’s classic mid/late‑1960s British pulp SF, originally published by Robert Hale and later in paperback (Ace), which fits your sense of age and tone.