Bank Deals

So I have to move a clients site to a new server, which isn't normally a problem. All the files and databases have been backed up, I just need to change the name servers. Up until this month, any time I changed a sites name servers, the change would reflect immediately in my browser. Now my ISP has decided that it needs to make me wait 24 hours until they refresh their DNS cache. I believe this is how it works anyways.. I can go to an anonymous browser and see the plesk config page, but in my browser I am still taken to the old site. I have tried flushing the DNS cache on my computer with no luck. It's really irritating as this is a site that I can not have any down time on. Now, last week I had to change another sites name servers and move the files, so I had to go war drive with my laptop until I found a wireless network. This would work this week but the site is about 36mb on disk and my laptops charging cord broke so I have no juice (the little pin fell out, long story).

Is there a way to force your computer to use a different name server for a site? Just using an anonymous browser  won't do it because it would take a week to upload 36 mb through a browser, so I need the change to reflect throughout my computer.

Better yet, being the noob that I am, maybe there is a way to upload to a plesk site before the name servers changes take effect? Like through the servers ip? Something like ftp://72.22.**.**/client/sitename/httpdocs/ ? Or something?

Oh, and about plesk, what folder is the stupid favicon stored in? I have a lot of clients using plesk VPS's/Dedicated and I'm sick of moving 10 or so sites there and then having to manually remove all the favicons it inserts. Some said use shell and go to xxx folder and you can remove it entirely?

okay I'm done ranting/whinning