A weapon is created throughout the duration, whether it’s solidified or dissipated. I don’t know why you default to “it doesn’t exist” when the rule says it absolutely exists.
Nothing says the dissipated shadow isn’t targetable. Maybe it’s like a small cloud of shadow waiting to be reformed. But either way, it still exists.
As I stated above, nothing in SB’s description states it’s invisible or otherwise undetectable when dissipated. If it is determined at a table to be invisible, I’d imagine the magic is still detectable by Detect Magic. Likewise, as you say, Dispel Magic doesn’t require the target to be seen, just that it’s within range.