And I finally, after ages of procrastinating on it, did a fewest skills attempt on No Time To Die. My best result so far: 29 skills.
It might be possible to reduce this to 24-ish. I'll try soon.
EDIT: Success. Reduced to 23 skills. This solution is VERY tight for time. The normal solution, I can do with about 7-8 seconds left on the clock. The 23 skills solution, 1 second remaining, on the edge of flipping over to 0.
Unless there's some way to pull off an awesome slide (which I haven't had much luck with), I'd say 23 is the bare minimum. I've tried a two-climber solution and it barely misses the time limit, so no luck there, besides, that was done based on the 29 skills solution so it probably wouldn't even work on the 23-skills one.
Still one hell of a lot of skills for a 2 minute, one screen, x of each skill level! (To be fair though, the level IS one of the hardest, if not THE hardest, so far... which is pretty amazing in itself for a one screen, x of each skill level...)