Choosing an optocoupler for a digital interface with old -ve polarity -5V electronics
I'd suggest that since you are unsure of the voltage and current levels on your switches (and you recognize that you don't have a lot of experience with electronics) you should use relays to activate your pushbutton circuits. 

There are plenty of small relay boards designed for microprocessors such as Arduino that would allow yo to simply solder in voltage free contacts across your existing pushbuttons.
For example for about $5 you can get a 4 relay board with opto-isolated inputs that will run from 5 V.


You might not need opto-isolation, and those variants are available too.  

Certainly this would seem to imply the absolute minimum of modification to your Telescope circuitry.