"Highly diluted" might be the key with Simple Green. I once noticed the label on the bottle said "do not use on leather". Watering it down might make it safe.
I use a 50/50 mix of Murphy's Oil Soap and water in a spray bottle. This is totally safe for leather and is something I picked up from my hobby of restoring antique and vintage baseball gloves. It also makes a good safe general purpose cleaner for all my other gear.
(Off the subject, but you can see some of my vintage gloves here:
The Glove Shop)
This mixture is used to clean/wipe down shoes after each game. Sometimes I'll use a small brush to get any gunk out of the nooks and crannies, in the seams, up under the tongue, around the laces, etc.
Besides that, I use plain old Kiwi black polish a few times a season, when needed. For touch-ups, and after each between game cleaning, I use one of those "quick shine" silicon sponges.
To keep the leather fresh and flexible, once or twice a year I completely clean the shoes with Lexol brand leather cleaner, then follow that up with an application of Lexol leather conditioner.