In Proto-Germanic the extended form *skeid- became *skītan "to separate, defecate" - ie "separate from the body" and then became Old English sċiten and English shit.
nice is from Old French from Latin nescius "ignorant", which is a combination of ne "not" and sciō.
*skei- is itself an extension of *sek- "to cut", the suffixed o-grade form of which, *sok-so-, became Proto-Germanic *saχsam "knife" (as in Old English seax "knife"), and possibly "swordsman" (as in Old English Seaxe, Old High German Sahsun, Icelandic Saxar, German Sachse "Saxon"). This was possibly borrowed into Latin as saxō "Saxon".
'This is a child!' Haigha replied eagerly, coming in front of Alice to introduce her, and spreading out both his hands towards her in an Anglo-Saxon attitude. 'We only found it to-day. It's as large as life, and twice as natural!'