As a layperson I can see how the Bengali numbers relate to those in European languages I can think of, but it has ‘choe’ where I would expect a sh- sound. What are the mechanics behind this ?
Following Hamp (1978, apud Blazek, Indo-European-Numerals) the Indo-Aryan forms require *Kswek's.
There's no unique solution.
Blazek sums that up pretty well, but doesn't spell it out and instead assumes prior *g'hes + *wek's, compounded to *g'hswek's, depalatized, because of the rule against two occlusives from the same series in a single root, thus giving plain *ks-.
This does not explain the absence of *K elsewhere, and perhaps because of that it found no wide acceptance, as far as I can tell.
The best evidence of *Ks- should be Avestan. Wiktionary, without admitting relevant references, reconstructs
Indo-Iranian: *šwáćš Indo-Aryan: *ṣwáṭṣ Sanskrit: षष् (ṣáṣ), षट् (ṣáṭ) Bengali: ছয় (chôy) ... Iranian: *xšwáš, *šwáš Avestan: 𐬑𐬴𐬎𐬎𐬀𐬱 (xṣ̌uuaš) ...
Blazek admits: "The absence of the initial cluster *šuu° in confrontation with the well documented cluster *xšuu° implies that also here x- is prothetic" [Blazek, PIE Num., pg. 241; with reference to Hoffmann, Forssmann Avestische Laut- und Flexionslehre, Innsbruck, IBS 84, 1996, pg. 103].
Not to mention that the semantics, "hand" + "grow", are merely hinted at and difficult to explain without any morphological glue. The existence of non-IE comparisons in at least Kartvelian, Hurrian, and Semitic (none with a *K) as well as an overall speculative understanding of the internal derivation of IE numerals don't exactly help the solution
I suppose the Balto-Slavic evidence with fricatives that could indirectly prove an initial velar ("there is no reason not to") would be due to areal influence upto common innovation.
Dissimilation from "seven" seems unlikely, if vice-versa the s- is under assumption of original *wek's- often assumed to be from analogy to seven.
Insofar the tangential Greek evidence remained to be explained it's just not overwhelming either. Note that initial s- was regularly lost in Greek (regarding other forms without s-). "also cf. Sarmatic *ksas".
It's not understandable why common innovation under the assumption of an appropriate timeline (including Indo-Aryan or not) came not into question. Prefigation obscured by any undetermined process would be one of the easier options, IMHO.
As far as the Aryan forms are concerned, let's note that in over 4000 Sanskrit lemmas indexed by wiktionary there are less than ten headwords under the initial ष, and all relate to "six" except one.
That one might reasonably be onomatopoetic, i.e. ष्ठीवति (ṣṭhī́vati) "to spit", though complicatedly rooted in PIE with diverse cognates, e.g. Lat. spuo, En. spew.
Refering to thorn-clusters and/or *kw > Greek p, t seems out of line so far. Yet, cp. Pashto spaz [with two haceks] ("six").
A reference to Aleks ~ diminutive Sasha s.v. and *h2lek'-s- ~ *h3reg'-s- "ruler" in view of the at least superficial similarity between Devangari "Sa", "Ra" and this one), insofar random, would be no less difficult to maintain.
The by-form Sanskr. shat "six" ("t- as in vit < *vits < *viks) matches the
Arabic sitt "6", sadis "6th", Hebrew šeš are deemed loans from IE [Blazek] whereas "seven" is deemed a loan into IE, of uncertain provinence [idem], but Blazek adopts a gloss "Siebenheit" for a Semitic *sab'átum, taken from >>*septmti "70" (orig. "Siebenheit"; cf. Debrunner & Wackernagel 1930: 369, 419; Mayrhofer 1996: 681 for ṣaṣṭí "60") […]<< [pg. 246, 256, 257].
Bengali and Pali forms do fit at least *ks-, but not *s-; Sanskrit does not fit any of them, as there's no comparable lexem. Although, it is taken as an example for Ruki Soundlaw.
Germanic too would permit *ks- > *(h)s-, too, although there's only one root and its derivatives for comparison (*kes-, *k-s-, cf. hair, Sw. snygg, etc).