Лифт вибрировал к остановкой на шестом этаже, и я достал в кармане для ключей, чтобы поискать ключ инженера для доступ на запретный этаж сверх, и свой аппарат. Был шум, будто кто-то кашлянул за мной. Я не обратил внимания, и продолжал шарить в кармане для подходящого ключа.

The lift juddered to a halt at the sixth storey, and I reached into my pocket to fetch the master key to gain access to the lift house (restricted floor, 'with it's machinery'?) above. There was a sound like someone clearing (or 'as if someone cleared') their throat behind me. I ignored it, and carried on fumbling (in my pocket) for the correct key.

'...сверх, и свой аппарат.' свой not in same clause as этаж, so is свой acceptable here?
'ключ инженера' No idea of Russian for 'master key'...
'подходящого ...' doesnt really mean 'correct', but I'm not sure what would in this context.

Had to edit a bit after posting, sorry. Too many bits missing.