、。
However, he wasn't seriously hurt — he got off with just a light bruise.
Literal
However, he [to-に] big injury [topic-は] not-exist, light bruise [with-で] was-settled.
けがはなく uses the contrastive は on the direct complement of ない — 'no big injury (though perhaps a minor one),' setting up the followup. The -く form of ない serves as a linking continuative 'and not X, then Y.' ~で済む 'to be settled with ~ / to get off with ~' is a set expression for the situation concluding with relatively minor consequences, often used after a potential disaster. 打撲傷 is a formal medical-ish term for 'bruise/contusion.'