I think a lot of the respondents here have missed this line in your OP.
That being the case (you’re not super concerned about isk/hr efficiency), any weapons system will be able to complete L4 missions without issue (given appropriate skills). Some will be easier than others, as turrets (long range ones, which are good for reaching out & touching the rats in L4 misisons) will have issues killing the elite frigates if they close on you (i.e. get into their orbit around your ship). Cruise missile based ships will be able to kill them eventually, no matter the range.
My suggestion would be to pick a ship you like the look of (have you seen the Nightmare? 
) and work towards that. The reason all the L4 fits include drones of some sort is because it can be easier to throw out 5x T2 light drones to take care of frigates while your missiles/turrets kill everything else. If you really do not want to use drones, ever, an option is to fly a ‘sniper’ fit, and keep everything outside 40km, and you need never launch drones again… I have drones on my Nightmare, but never use them cause it’s easier to just shoot things with the lasers!
Edit: This is a fit I’ve posted before, it still works.
Regards,
Cypr3ss.