You must be using a lot of cannon shells to get through shields, Is more efficient if you get two lasers and two cannons you can use your lasers to take down shields and cannons on the hull
Think of the "modes" more as groups, if you go to your right hand display you can set up fire groups so in this case set your lasers to one group and cannons to another and maybe another group with both....you can then bind a key/button to switch your groups
Docking computers are nice for the first couple of runs but the soon get boring as you can get in much quicker without them, and you defo do not want to be running narcotics and using a DC, you will get scanned and fined in short order