He could hold the power stone and not explode. He has been shown to be resistant to mind control and could get most of the stones without any trouble.
The only problem would be the soul but you forget that some people would have no problem sacrificing themselves for superman. Jimmy Olsen would do it without a second though. Superman would not let him but Jimmy would jump.
Course Superman could collect all the infinity stones. The Power stone might know him with a 24 second bug after collecting it, The Tesseract is encased in a cube though that isn't a problem, And finally, Could Clark Kent murder the person he loved most to get his hands on the soul stone? Or is he strong enough to break that rule and get away with it?
I think he is capable of obtaining the stones, But he is too much of a paragon to kill someone, Especially someone he loves. If he waited for someone else to collect it, He could then theoretically steal it from them but I assume that's not the object of the argument.