The List
There are 305 4 letter words with C as the first letter. The highest scoring is COZY at 18 points in Scrabble. 2 of them contain no vowel at all: CWMS, CYST.
CAASCABACABSCACACACKCADECADICADSCAFECAFFCAGECAGSCAGYCAIDCAINCAKECAKYCALFCALKCALLCALMCALOCALPCALXCAMACAMECAMOCAMPCAMSCANECANGCANNCANSCANTCANYCAPACAPECAPHCAPICAPOCAPSCARBCARDCARECARKCARLCARNCARPCARRCARSCARTCASACASECASHCASKCASTCATECATSCAUFCAUKCAULCAUMCAUPCAVACAVECAVYCAWSCAYSCEASCECACEDECEDICEESCEILCELLCELSCELTCENSCENTCEPECEPSCERECEROCERTCESSCETECHADCHAICHALCHAMCHAOCHAPCHARCHASCHATCHAVCHAWCHAYCHEFCHERCHEWCHEZCHIACHIBCHICCHIDCHIKCHINCHIPCHISCHITCHIVCHIZCHOCCHOGCHONCHOPCHOUCHOWCHUBCHUGCHUMCHURCHUTCIAOCIDECIDSCIELCIGSCILLCINECIONCIRECIRLCISTCITECITOCITSCITYCIVECLADCLAGCLAMCLANCLAPCLATCLAWCLAYCLEFCLEGCLEMCLEWCLIPCLODCLOGCLONCLOPCLOTCLOUCLOWCLOYCLUBCLUECOALCOATCOAXCOBBCOBSCOCACOCHCOCOCODACODECODSCOEDCOFFCOFTCOGSCOHOCOIFCOILCOINCOIRCOITCOKECOKYCOLACOLDCOLECOLLCOLSCOLTCOLYCOMACOMBCOMECOMMCOMPCOMSCONDCONECONFCONICONKCONNCONSCONYCOOFCOOKCOOLCOOMCOOPCOOSCOOTCOPECOPSCOPYCORDCORECORFCORKCORMCORNCORSCORYCOSECOSHCOSSCOSTCOSYCOTECOTHCOTSCOTTCOUPCOURCOVECOWKCOWLCOWPCOWSCOWYCOXACOXYCOYSCOZECOZYCRABCRAGCRAMCRANCRAWCRAYCREDCREECREMCREWCRIACRIBCRIMCRISCRITCROCCROGCROPCROWCRUDCRUECRUSCRUXCUBECUBSCUDSCUEDCUESCUFFCUIFCUITCUKECULLCULMCULTCUPSCURBCURDCURECURFCURLCURNCURRCURSCURTCUSHCUSKCUSPCUSSCUTECUTSCWMSCYANCYMACYMECYSTCYTECZAR