I can't comment on Shaw's book, haven't read it. And I can't read Arabic, Hindi or Urdu, so can't pronounce on Alam Khan's linguistic analysis. However, the article seems pretty correct in discounting claims for very early use of artillery in India. It does seem that though there is evidence for gunpowder appearing in India for fireworks by the mid-1300's, the first undeniable evidence for artillery is in a painting circa 1476 done during the reign of Sikandar Lodi.

This pretty much mirrors the appearance and use of such things in the Ottoman Empire and Europe. Very simple formulations of unrefined saltpeter with charcoal and sulfur will make fireworks, and there's a good bit of evidence for such things going very far back, first in China. But it was not until the 14th c. that real advances were made in the refining of saltpeter and the manufacturing of gunpowder that created a consistent propellant, after which aimed weapons became possible. Also, even when small arms and aimed cannon appeared in the 15th. c ( as opposed to things that could only be fired towards walls) , nomadic groups didn't find them particularly useful: it was pointless to drag a cannon around on the steppes, where there were few citadels or fortified towns to attack, and loading and firing muzzle-loading matchlocks on horseback is very, very awkward, compared to using a bow and arrows. Though there's a chance the Mongols brought gunpowder to India quite early, there are much stronger links to the Ottomans, when the use of real artillery proliferates there in the 16th c.

Chase, K. (2008). Firearms: A Global History to 1700 (1st ed.). Cambridge University Press.