The List
There are 211 4 letter words with W as the first letter. The highest scoring is WHIZ at 19 points in Scrabble. 5 of them contain no vowel at all: WHYS, WYCH, WYND, WYNN, WYNS.
WAACWABSWACKWADDWADEWADIWADSWADTWADYWAESWAFFWAFTWAGEWAGSWAIDWAIFWAILWAINWAIRWAISWAITWAKAWAKEWAKFWALDWALEWALIWALKWALLWALYWAMEWANDWANEWANSWANTWANYWAPSWAQFWARBWARDWAREWARKWARMWARNWARPWARSWARTWARYWASEWASHWASPWASTWATEWATSWATTWAUKWAULWAURWAVEWAVYWAWAWAWEWAWLWAWSWAXYWAYSWEAKWEALWEANWEARWEBSWEDSWEEDWEEKWEELWEEMWEENWEEPWEERWEESWEETWEFTWEIDWEILWEIRWEKAWELDWELKWELLWELSWELTWEMBWEMSWENAWENDWENSWENTWEPTWEREWEROWERTWESTWETAWETSWEXEWEYSWHAEWHAMWHAPWHATWHEEWHENWHETWHEWWHEYWHIDWHIGWHIMWHINWHIOWHIPWHIRWHITWHIZWHOAWHOMWHOPWHOTWHOWWHUPWHYSWICEWICHWICKWIDEWIELWIFEWIGSWIKIWILDWILEWILIWILLWILTWILYWIMPWINDWINEWINGWINKWINNWINOWINSWINYWIPEWIREWIRYWISEWISHWISPWISSWISTWITEWITHWITSWIVEWOADWOCKWOESWOFSWOGSWOKEWOKSWOLDWOLFWOMBWONKWONSWONTWOODWOOFWOOLWOONWOOSWOOTWOPSWORDWOREWORKWORMWORNWORTWOSTWOTSWOVEWOWFWOWSWRAPWRENWRITWUDSWUDUWULLWUSSWYCHWYESWYLEWYNDWYNNWYNSWYTE