'what would she have done if someone had discovered the bow and retrieved her fingerprints on it?'
Well, thing is nobody discovered it. It was a party of elite people gathered together annually to renew their vows or sumthin' regarding the secret/s they have to keep for the rest of eternity? One does not simply check boxes lying around on a corner if they have nothing to do with it. Even if someone else (not Conan or any detective geek) has seen what was inside the box say, before the incident, I don't think one will make a fuss over it since it was just a crossbow (a gun or bombs on the other hand...). On second thought, since we're talking about what would happen if someone saw the bow BEFORE the murder, they would also see the poisoned ice pick loaded in it. But then again, the culprit herself was near the weapon so she would just shoo away anyone who is too curious to check the box for no reason. AND IF someone discovered what's inside the box AFTER the incident, investigators will try to check it out if it's related to the case BUT REMEMBER that the initial suspected weapon was the ice pick. It was only through Conan that we know that the crossbow is actually related to the murder since we have inspected something peculiar with the ice pick itself. Also, the island they're on doesn't even have any other policemen aside from the one we met. Someone had to call in a superintendent from the mainland to investigate a special case. Who knows if there is even a hospital in the island (Though I'm probably thinking about the other island when I'm saying this... Haven't finish the game yet...). Anyway, point is, retrieving her fingerprints will also take a while due to lack of forensic investigators. Unless you were talking about her fingernail..?
'I don't even understand how anyone, especially the bartender, didn't check inside the wooden box'
Hmm... Good point. However, keep in mind that the person who actually crafted the murder trick was that waiter posing as 'Higure' (don't remember what his waiter name was... or other name whatever). Maybe he has been a waiter in that hotel long enough to know what usually happens in the annual parties. Including knowing that the bartender highly respects his job and the liquors around him. This just came to mind, but what if there is always a box placed there whenever there's an event which supposedly always contains wine, as a backup for if the bar runs out of booze? And since the party didn't even finished, all the food were wasted and not all the drinks were used. Which explains why the box was untouched. If I'm remembering correctly, wines/liquors tastes better if they have been stored for a very long time. So, all the more reason not to touch the box. Eventually, it will be found out when the bartender finally decides to arrange the wine that's supposedly in the box, on the cellar. Though, by that time, if no meddling kid have interfered with the case, the murderers would have probably disposed off of the real weapon already.