I feel like this is a common question people have when they first learn about the labiovelar series, but none of these answers are very satisfying.
As said, if we can't find a direct difference in reflexes, then we might look for differences in behaviour: we would always expect to see *kʷ as *kʷ, but *kw would, in certain circumstances, become *ku instead. The bare fact that *kʷ doesn't so disintegrate isn't enough—we need demonstrated (not just theoretical) evidence that *kw does.
And if we can't find any instances of *kw because plain velars are so rare to begin with, we could look to *ḱw instead, since all of the centum languages collapsed the palatovelar series into the plain velars. Centumisation happened post-PIE, so we might have to add a few extra caveats to our conclusions, but whatever.
But what we can't do is look for alternation between *ḱw and *ḱu and take that as evidence of a contrast between *kw and *kʷ unless we can also show that this alternation happened post-centumisation, otherwise we've only demonstrated a contrast between *ḱw and *kʷ, which I don't think anyone doubts. The alternation present in the paradigm of *ḱwṓ certainly predates centumisation, so it's not relevant, and *h₁éḱwos doesn't show any alternation at all. Really, only evidence of different outcomes of *kʷ and *ḱw themselves would do, and there is none (Sihler's ἵππος notwithstanding).
There is, however, a controversial root *kwep- 'to smoke, steam', which is apparently attested in the full-grade in Latvian kvêpt 'to smell', kvêpêt 'to smoke', and Lithuanian kvė̃pti 'to smell' (and a bunch of other languages in other grades: Latvian and Lithuanian aren't the only basis for this root's existence). If you accept this root, that's your smoking gun: Latvian and Lithuanian are satem languages, so they turned their labiovelars into plain velars, but here they preserve PIE *kw as /kv/ or /kʋ/ instead of /k/. Direct evidence of different outcomes.
(That root also shows the predicted alternation between *kw in the full-grade and *ku in the zero-grade, but we don't even need it now.)