The List
There are 469 6 letter words with H as the last letter. The highest scoring is HUZZAH at 30 points in Scrabble. 1 of them contain no vowel at all: FLYSCH.
AARRGHABEIGHABLUSHACANTHAFRESHAGUISHAGUNAHAKEDAHALIYAHAMBACHAMBUSHANARCHANEATHANKUSHANOUGHAREACHARRISHASLOSHASPISHATTACHAVOUCHAWATCHAWEIGHBABLAHBANISHBARISHBEDASHBEEGAHBEENAHBESIGHBIFTAHBLANCHBLEACHBLENCHBLOTCHBLUISHBODACHBORSCHBOYISHBRANCHBREACHBREATHBREECHBROACHBROOCHBROUGHBRUNCHBYPATHCALASHCALIPHCAMASHCAROCHCASBAHCERIPHCHALAHCHALEHCHETAHCHINCHCHOUGHCHOUSHCHURCHCLATCHCLENCHCLEUCHCLEUGHCLINCHCLOUGHCLUNCHCLUTCHCOHOSHCOMETHCOOLTHCOOTCHCOPRAHCOSECHCOWISHCOYISHCRANCHCRATCHCREACHCREAGHCREESHCROTCHCROUCHCRUNCHCRUTCHCULTCHCURAGHDALEDHDALETHDANISHDARGAHDAWISHDEARTHDEBOSHDELISHDETACHDIARCHDOODAHDOTISHDOURAHDOVISHDREICHDREIGHDRENCHDRIEGHDROICHDROUTHDRYISHDUDISHDUKKAHDURGAHEADISHEDDISHEIGHTHELENCHELFISHELVISHEMDASHEMMESHENARCHENCASHENDASHENMESHENOUGHENRICHEOLITHEPARCHERIACHEXARCHFAMISHFATWAHFELLAHFETICHFETISHFIKISHFINISHFLANCHFLEADHFLEECHFLENCHFLETCHFLINCHFLITCHFLOUSHFLUISHFLYSCHFOGASHFOURTHFRATCHFRENCHGALOSHGALUTHGAMASHGANJAHGARISHGAUNCHGEEZAHGLITCHGLUISHGLUNCHGOLOSHGONOPHGOYISHGRAITHGRINCHGROUCHGROUGHGROWTHGRUMPHGRUTCHGUBBAHGUNYAHGURRAHHADITHHAINCHHAJJAHHALLAHHALVAHHAMZAHHARISHHAUNCHHEALTHHEARTHHIGHTHHIJRAHHOOKAHHOORAHHOOTCHHOUDAHHOWDAHHUPPAHHURRAHHUZZAHIBADAHIMMESHIMPISHINARCHINMESHINRUSHINWITHJADISHJARRAHJIBBAHJOSEPHJUBBAHJUBHAHKALIPHKASBAHKEBLAHKEDDAHKHEDAHKIAUGHKIBBEHKIBLAHKIBOSHKIRBEHKIRSCHKITSCHKLATCHKLOOCHKNITCHKOOLAHKVETCHKYBOSHLAKISHLAMEDHLAMISHLATISHLAUNCHLAVASHLAVISHLENGTHLINISHLIROTHLOOFAHLOWISHMARISHMATSAHMATZAHMATZOHMENSCHMIKVAHMIKVEHMINISHMODISHMOLLAHMOLOCHMONETHMONISHMOOLAHMOPISHMORISHMORYAHMULISHMULLAHNALLAHNAUTCHNEBISHNEWISHNICISHNULLAHNUMDAHNUMNAHOAFISHODDISHOFFISHOGRISHOLDISHOLLAMHONRUSHOOLITHOOMPAHOWLISHPAINCHPALISHPALLAHPAPISHPARAPHPARDAHPARIAHPARISHPAUNCHPERISHPHWOAHPLANCHPLEACHPLENCHPLEUCHPLEUGHPLINTHPLOUGHPOLISHPOOJAHPOPISHPOTASHPREACHPRUTAHPUNISHPUNKAHPURDAHPUTSCHQUAICHQUAIGHQUATCHQUEACHQUELCHQUENCHQUETCHQUITCHQURUSHRADISHRAKISHRAUNCHRAVISHRAWISHREHASHRELISHREWASHRUDISHRUPIAHSAKIEHSAMECHSAMEKHSCAITHSCARPHSCARTHSCATCHSCOOCHSCOOSHSCORCHSCOTCHSCOUTHSCOWTHSCULCHSCUTCHSEALCHSEALGHSEARCHSECESHSERAPHSERIPHSHAIKHSHAUGHSHEATHSHEESHSHEIKHSHEUCHSHEUGHSHIBAHSHIVAHSHOUGHSHYISHSIRRAHSIWASHSKAITHSKARTHSKEIGHSKETCHSKITCHSKOOSHSKYISHSLATCHSLEECHSLEIGHSLEUTHSLOOSHSLOUCHSLOUGHSLUTCHSLYISHSMATCHSMEATHSMEECHSMEETHSMIRCHSMOOCHSMOOSHSMOOTHSMOUCHSMUTCHSNEATHSNEESHSNITCHSPARTHSPEECHSPETCHSPILTHSPLASHSPLISHSPLOSHSPRUSHSQUASHSQUISHSQUUSHSTAITHSTANCHSTARCHSTENCHSTITCHSTOUSHSTOUTHSTRATHSTRICHSUCCAHSUKKAHSUMACHSUNNAHSWARTHSWATCHSWITCHSWOOSHTAISCHTANNAHTASBIHTEMPEHTERAPHTHANAHTHATCHTHETCHTHOUGHTHRASHTHRESHTHRUSHTONISHTOROTHTOYISHTREFAHTRENCHTROUCHTROUGHTROWTHTUSSAHTUSSEHTWITCHTYKISHUNEATHUNLASHUNLICHUNMESHUNWISHUPGUSHUPPISHUPRUSHVANISHVARECHWAIRSHWALLAHWARMTHWEALTHWHEECHWHEESHWHEUGHWHIDAHWHOOSHWHYDAHWIDISHWINISHWIRRAHWRAITHWREATHWRENCHWRETCHWROATHZENITHZEROTHZIBETHZILLAHZIZITH