The relevant kind of "ability to use tools" is whatever can be used, however inefficiently at the beginning, to start building stuff, if you apply the ingenuity of an international scientific community for 100000 years to the task; not appendages that a chimp-level chimp can use to sharpen sticks in an evening. You seem to underestimate the power of intelligence.
This is directly analogous to AI boxing, with limitations of intelligent creatures' bodies playing the role of the box. I'd expect intelligent tortoises or horses should still be capable of bootstrapping technological civilization (if they get better than humans at rationality to sustain scientific progress in the initial absence of technological benefits, or just individually sufficiently more intelligent to get to the equivalent of the necessary culture's benefit in a lifetime).
There are a lot of species that are almost as smart as humans, and some even engage in tool use. (e.g. many species of corvids). But their tool use is limited, and part of the limit appears to be their lack of useful appendages and comparatively small size. In at least some of these species such as the New Caladonian Crow, tool techniques can be passed on from one generation to the next. This sort of thing suggests that appendages matter a fair bit.
(Obviously they aren't sufficient even when one is fairly smart. Elephants have an extreme flexible appendage, have culture, are pretty brainy, and don't seem to have developed any substantial tool use.)
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