No not really. They don't make a difference.

What could make a difference is whether or not the old Soviet nukes have actually been maintained and actually work. Not something one wants to test but it would make for some great sci fi to imagine the missiles launch, everyone clenches their butthole, and when everything's over, Russia is a crater in the ground and the west is fine.

edit: for reference hypersonic missiles tend to refer to the shorter range stuff. All the ICBMs of old were already hypersonic.