Contrary to his 'not bad-looking but a bit flaky' appearance, he has no girlfriend and isn't even quick with women.
Literal
''Appearance [topic-は] bad-not but a-bit flimsy-seeming'' [attributive-な] appearance [with-とは] contrary-to, girlfriend [subject-が] not-exist-[and-し], women [locative-に] hands [subject-が] quick reason is-not.
A character description. ~とは裏腹に is a fixed literary expression meaning 'contrary to X', 'despite the appearance of X' — literally 'inverse to X'. 軽薄 (けいはく) means 'flaky, frivolous, superficial' — literally 'light-thin'. 手が早い ('hands are quick') is an idiom meaning 'quick with women' — promiscuous, a womanizer. ワケでもない ('it's not even the case that') is a soft concessive negation.