Does any living language contrast /kʷ/ and /kw/?
If yes, is there a way I can hear a minimal pair spoken?
In theory, yes. Tashlhiyt Berber is said to have a contrast, but that does not mean that there are any minimal pairs. That article points to literature, saying that it is generally agreed that they are different. However, the article slightly undermines the claim by noting that [kw] and [kʷ] differ in terms of syllabification: which (potentially) means that the distinction is not [kʷ] vs. [kw], it resides in distinctive syllabification. That means that it depends on what you mean by "minimal pair". Tigrinya has a similar potential, that k+w sequences can be constructed and there is a /kʷ/ phoneme, but the actual phonetic values have other low-level properties associated with the sequence vs. single segment. In both cases, there's a good argument that kw is different, phonologically, from kʷ, but I suspect that minimal pairs are a deal-breaker.
Thai can be what you are looking for.
It has onset clusters /kw/, /kʰw/. Quite often, they are realized as labialized velar consonants /kʷ/, /kʰʷ/.
However¹, final stops like /-k/ are accompanied by a simultaneous glottal stop, thus making syllable boundaries well defined by intersyllabic juncture. This prevents any C-to-C coarticulation and resyllabification of final consonants.
So if there are two adjacent syllables, one ends with the final /-k/ and another starts with /w-/, they remain audibly separate.
Compare (press 🔈 speaker icon to listen):
- ทุกวัน
[tʰúk wan]"every day" - กวาง
[kwaːŋ]"deer"
