I mean, honestly, Silver, and telekinesis in general, acts as a fantastic counter to Danmaku. That's Silver's primary use of his telekinesis, to pick up things and hurl them at folk. If she's just hurling stuff at Silver, then he'll just hurl it back at her with even more force. The whole thing about how many she can toss out is rendered moot just by the fact that Silver's power is a perfect counter to this, the fact that speed is equalized, and the fact that he can plunk many of them out of the air, and hurl them before they get too close. His telekinetic range is farily bad, yes, but as super silver it's pretty good given that he's fighting in space. And against Iblis at the end of his story, it was also fairy decent. He's even capable of catching sonic mid homing attack, so I mean, hurling stuff at him is overall just not all that effective.
I'm fairly certain that needing the rings is just a game mechanic, as that would likely not be applied to a real fight. And in the cutscene, he didn't need them to maintain his form. Only the chaos emeralds were needed to unlock the form. Once the battle was done, he was able to go back into base form on his own.
All this being said, he still can't get past low godly regen. And even in character, Silver fights to kill, so knocking her out isn't really an option for him. His powers, while perfectly suited to combat her danmaku, provide him no way of putting her down permantently, hence my inconclusive vote.