Did Shakespeare influence the KJV in Psalm 46?

Some critics claim that Shakespeare left his mark in the 1611 KJV by inserting in Psalm 46 the words “shake” (v. 3) and “speare” (v. 9).  This is one of the most ignorant charges against the KJV.  The Bishop’s Bible of 1568 has “shake” and “speare” in Psalm 46.  Shakespeare was still an infant when the Bishop’s Bible was published.  Surely an infant cannot influence a Bible translation.

Bishop's Bible - Psalm 41:3-9:
3 Though the waters thereof rage and swell: and though the mountaynes shake at the surges of the same. Selah. 4 [Yet] the fludde by his ryuers shall make glad the citie of God: the holy place of the tabernacles of the most hyghest. 5 God is in the myddest of her, therfore she can not be remoued: the Lorde wyll helpe her, and that ryght early. 6 The heathen make much a do, and the kyngdomes are moued: but [God] shewed his voyce, and the earth melted away. 7 The God of hoastes is with vs: the Lorde of Iacob is our refuge. Selah. 8 O come hither and b9 He maketh warres to ceasse in all the worlde: he breaketh the bowe, & knappeth the speare in sunder, and burneth the charettes in the fire.