Sorry, saying my hands were shaking from the cold was a bit of an exaggeration.
Literal
Hands [subject-が] cold [because-で] shook [topic-は], a-little over [copula-で] sorry.
A self-correction. 手が寒さで震えた ('my hands shook from the cold') is quoted as the topic with は — 'as for (having said) my hands shook from the cold.' オーバー is the katakana loanword 'over' (from 'overacting' / 'overstated'), here a na-adjective meaning 'exaggerated.' すみません ('sorry') closes the apology. The combination is a live self-correction in speech.