I recently found myself in the same situation, took some RAW shots, not RAW + Jpeg, and now have a ton of photos that I need to improve in order to show anyone.
I've tried a small handful of programs so far- Imaging Edge, Fotor, FastStone Image Viewer.
Here's what I've found-
Imaging Edge works very well. It's made by Sony and going by the logic that "Sony knows Sony", I trust that it knows how to work with it's own camera's images. And the results look pretty good. It's also reasonably fast, 500 pictures took around 30-40 minutes.
FastStone Viewer was nearly as good. I used the "Quality = 100" setting, everything else default. It was as fast, or nearly as fast, as Imaging Edge. The quality was nearly indistinguishable. The jpeg file sizes were much larger, around double the size. FastStone has some other options that could be tweaked that might make more of a difference, but I didn't play with them.
Fotor was not very good. It was VERY slow, taking about 24 hours to convert the photos (it's hard to tell exactly how long, because my laptop kept sleeping after a few hours, and I'm not sure the processing was working in the background.) Also, the resulting photos were very 'noisy'. Some looked ok at the regular size, but when I zoomed in on the photo, there were a LOT of extra color and pixels that distracted from the image. Would not recommend this one.
So, as Michael C says, try the Sony program and see what happens. Imaging Edge is actually three programs (viewer, editor and camera remote control). It's the viewer that I used to batch-output my photos.
Hope that helps.