What you DON'T want to try to do, if it blows up (or seems to be), is some Hail Mary hack-in-somehow-and-try-to-save-the-day. If the update doesn't work and you weren't given the login, you have an eminently reasonable excuse for why you could not save the day.
On the other hand, if you somehow mess with things in a desperate attempt to fix it, and somehow make matters worse, you could be considered to have made a mistake.
Either way, if things blow up, you will have to go to your boss's boss and explain that you don't know how to fix it and don't have a login to attempt to do it even if you did. You will want to do this calmly and professionally, not going out of your way to make anyone else look worse (not that this would be necessary anyway, from the sound of it), but being clear about the actual situation.
Your boss apparently thinks this update is trivial, and will require nothing of you. Perhaps he is right. If he is not, then if you have not been prepared to troubleshoot you could easily make things worse, so be plain and clear about your inability to fix something you haven't been briefed on. They will have to either get hold of your boss, or else call the company who makes the software, and perhaps in that case they may be able to walk you through what to do. If not, don't pretend to knowledge you don't have.
Have a good weekend, you have done what you can do by voicing concern.