Shave
Old English sc(e)afan ‘scrape away the surface of (something) by paring’, of Germanic origin; related to Dutch schaven and German schaben .
wiktionary
Inherited from Middle English shaven, schaven, from Old English sċafan(“to shave, scrape, shred, polish”), from Proto-Germanic *skabaną(“to scratch”), from Proto-Indo-European *skabʰ-(“to cut, split, form, carve”). Cognate with West Frisian skave, Dutch schaven(“to shave, plane”), Low German schaven(“to scrape, scratch, shave”), German schaben(“to scrape, shave”), Danish skave, Norwegian Nynorsk skava, Swedish skava(“to scrape, chafe”), Icelandic skafa, Gothic 𐍃𐌺𐌰𐌱𐌰𐌽( skaban, “to shear, shave”).
From Middle English shave, from Old English sceafa, from Proto-Germanic *skabô.
etymonline
shave (v.)
Old English sceafan (strong verb, past tense scof, past participle scafen), "to scrape, shave, polish," from Proto-Germanic *skaban (source also of Old Norse skafa, Middle Dutch scaven, German schaben, Gothic skaban "scratch, shave, scrape"), from PIE *skabh-, collateral form of root *(s)kep- "to cut, to scrape, to hack" (see scabies). Related: Shaved; shaving. Original strong verb status is preserved in past tense form shaven. Specifically in reference to cutting the hair close from mid-13c. Figurative sense of "to strip (someone) of money or possessions" is attested from late 14c.
shave (n.)
c. 1600, "something shaved off;" from shave (v.); Old English sceafa meant "tool for shaving." Meaning "operation of shaving" is from 1838. Meaning "a grazing touch" is recorded from 1834. Phrase a close shave is from 1856, on notion of "a slight, grazing touch."