If this was a warship, there would also be alternative trauma stations in those sections away from sickbay, basically a wall cabinet that opens up to reveal a fold-down treatment table, with portable med gear and meds tucked  on shelves on either sides of the beds, and lamps that switch to battery should power be disrupted.

The dining area would be a perfect place for one, but I suspect it's also next to both hiberation and sick bay.

Likely what's available is a large med cabinet that can be found in the cargo hold, engineering, and bridge. Near the hatch.