Mechanical computers exist - assuming that the calculations are standard, you'd likely have standardised mechanical devices meant to do *parts* of calculation and do the rest by hand. Navigation/position taking with starcharts (which is where it gets complicated. these things would be bulky and depend on your region of space, and sexants for taking readings). 

I like the idea of charts and a whole rack of numbered *[curtas][1]* - you have a manual telling you which ones to use and you'd basically start with #1, do calculations, pass on the values to a second and so on.

Something worth considering is the classic starships were small and cramped. Having to carry charts on paper and mechanical calculators might be something plotworthy, Perhaps having your navigator's quarters described as 6 walls of chained down books, and a wall of mechanical calculators, kept in zero G for easy access 


  [1]: https://en.wikipedia.org/wiki/Curta