HG500 10 speed has a very nice 11/42T, you really may need the largest cog, I had 11 36 and not happy with it when I climbed steep hills, 42 makes a big difference.
I agree that sg can be very good at cleaning drivetrain on the bike and probably safe as long as rinsed. But there is an aircraft version which is safe and just a bit more expensive so I may go for this for general cleaning for peace of mind.
https://www.amazon.com/Simple-Green-Extreme-Aircraft-Precision/dp/B081D5R6T9
My problem is stripping the chain from all the lube efficiently for waxing and I am not sure if this will work for that purpose.
Edit: I should also mention I tried regular Simple Green to strip the chain of factory lube but unfortunately it didn't work while Finish line worked well. On the other hand for getting rid of grease/grime on the chain, cogs etc. simple green worked very well on an old chain. (So the extreme version can be a great budget and safe cleaner for most people's needs).