ski is borrowed from Norwegian ski, from Old Norse skið "snow-shoe, billet of cleft wood". This is from Proto-Germanic *skītan "to separate, defecate" from Proto-Indo-European *skei- "to cut, split" (written about before by me).
According to the AHD, shyster is probably from the same Proto-Germanic form, from German Scheißer "son of a bitch, bastard" from scheißen "to defecate". But the OED says "of obscure origin".
Modern Norwegian ski is pronounced like she, but presumably the form that was borrowed into English was pronounced with /sk/. In the Mystery Science Theater 3000 short "Snow Thrills" we are told that the correct pronunciation of skiing is "she-ing". To which Joel responds "Yeah, well you're full of skit."
Proto-Germanic *sk- becoming /sk/ in some languages and /ʃ/ in others gives us some cool doublets, for instance:
scatter - shatter
skiff - ship
skirt - shirt
skit - shit
scot(-free) - shot
screed - shred
scuffle - shuffle