You should never have two antivirus products on your PC at once, so you're right to uninstall McAfee.
Viruses don't come out of thin air. They only arrive via the internet or via external media. So you can use any PC, without any virus protection at all for as long as you like, with no risk whatsoever as long as you're not connected to the internet and don't use any suspect external media.
If your new product is on a disk (from a reputable source), simply disconnect from the internet, uninstall McAfee and install the new software from the disk.
If you need to download the software, do so before uninstalling McAfee. (You'll only be downloading the new installation program onto your PC. You won't yet have the new antivirus program installed, so there will be no conflicts between the two products). Then disconnect from the internet, uninstall McAfee and run the installation program which you've downloaded.
Chris