I am much like you. Programming is a necessary evil for me, but I do not enjoy it. I have no formal training in CAD programs, but had to learn it to realize my projects. I am comfortable mostly in the world of electronics. But, with so many interests such as animatronics, I had to learn sewing, sculpting, casting, molding, and other numerous skills.
But, you just hit on the number one reason I am upgrading my laser cutter. I want to use the RAMPS controller so that I can open up the possibilities of software. Once upon a day, people wrote the G-Code entirely by hand. Still entirely possible to do, but not fast or simple. Not something I would even want to learn to do! But of course, we are forced to know it enough to diagnose problems with our toolpaths and to understand what the machine is doing.
I use Sketchup almost entirely for my design work and openscad for some things it does better. Its probably silly (my fried thinks so anyway) but the number one reason I like Sketchup is the guide lines. It just makes sense to me in a natural way. And with a ramps controller, I should be able to use Sketchup even for the laser cutting designs.
Anyway, back to slicers. I use Simplify3D for my 3D printing. It has its own propietary slicer. I used Cura and Repetier-host previously on my Solidoodle. I liked Cura much better than Slic3r, but some things Slic3r did better. It really depended on the model. This printer is a makerbot/flashforge clone, so it uses x3g which a binary g-code. It really limits what software I can use, but Simplify3D seems to work well with it (after some headaches setting it up.)
And as Elaser says, the ability to import DXF is a definite. Most of my work with the laser will be panel cut outs, enclosures, etc... So, using CAD programs is a requirement. Thankfully I do know Inkscape and Corel a little from a former life doing desktop publishing. But it is definitely not my preferred tool.