I think it is eathly seen that snape is the primary descendant from ON snepya. See the Online Etymology, snape, ME snaip, snaipen, snape are the intermediate forms.
From Middle English snape, snaipen (“to nip, injure, afflict; cold, nipping; to rebuke, revile, criticize”), from Old Norse snepya (“to outrage, dishonor, disgrace”).
Verb - snape (simple past and past participle snaped)
1. (Shipbuilding) To bevel the end of a timber to fit against an inclined surface. 2. to nip, injure, afflict
- Þe snawe snitered ful snart, þat snayped þe wylde. — Sir Gawain and the Green Knight
3. to be hard upon, rebuke, snub, criticize
- Vte of desert þar he was in, He com to snaip þe king sinn. — Cursor Mundi, 1400
- To Snape: corripere — Catholicon Anglicum, 1483
- He saw nothing, heard nothing, rushed on, he knew not whither, snaping, and uttering hoarse cries. — John Esten Cooke, Out of the Foam, 1871
- He saw nothing, heard nothing, rushed on, he knew not whither, snaping, and uttering hoarse cries. — John Esten Cooke, Out of the Foam, 1871
- The colnel (sic) I dont think like him much. I undirstand (sic) he was always snaping him. — Terry A. Johnston, Him on One Side and Me on the Other, Univ. of South Carolina Press, p48, 1999 (quoting Alexander Campbell, 1861)
- I imagine her prodding my flab and snaping, "There's nothing there — get rid of that!" — Joan Raphael-Leff, Pregnancy: The Inside Story, Karnac Books, p22, 2001