If I couldn't use CA and accelerator I would abandon my hobbies. Call it addiction if you want, but CA+ACelerator rocks my world.
But there are accelerators, and accelerators. I have tried about half a dozen brands over the years. Some work better than others. Some are slower or faster acting, and some (like Zip-Kicker for example) will attack styrene (which is what I bond most of the time).
At this point I have settled on the BSI accelerator as my favorite. Very low odor, does not evaporate too fast, and it is slower acting than other brands.
The way I use it I have not seen any glue joint weakening either. I should also mention, that the less viscous the CA glue is, the faster will the accelerator kick it over. I also never spray the accelerator - I use Micro Brushes to apply it.