Datapoint Michif/kʷ - labialized voiceless velar plosive
The sequence /kw/ can be used initially and word-medially, as in eekwa 'and', kwaapaha 'bail water' in words of Cree origin, but apparently only in initial syllables in words of French origin. (kwarnee 'crow'). It cannot be found word-finally.
The sequence stop-w for Cree, French and Michif has usually been analyzed as a sequence of a stop + /w/, but there are good arguments for analyzing them as labialized stops, at least for Michif.
(1) Etymologically French words starting in ko- frequently labialize the velar, e.g. Michif kwarik, French korek(t) 'correct'; kwachiiiy 'sea shell' (French: /kokiy/), suggesting a productive rounding process in ko- (but not in ku-).
This process is only occasionally found in etymologically Cree words, as in pikwawna / piko ana 'anybody'. The alternation between labialized velars and plain velars preceded by a back vowel is found in many Algonquian languages.
(2) In some cases /kw/ and /k/ are pronunciation variants, as one hears both kwasee and korsee 'girdle', kwarnee, kornee.
(3) Forms like chwizin for 'kitchen', in which the original /k/ is palatalized, suggest that /kw/ is a unit, as the velar is affected by a palatalization process under the influence of the high front vowel. The forms chwiizinn and kwiizinn are both used.
Values 
Exists (as a major allophone)
- Example 75-303:
-
kwashoon - kwayeshpig - right