No, you will not need to reinstall Windows as uninstalling/reinstalling VMware Fusion does not delete the Virtual Machines.
First you need to change the Hardware Compatibility so as to run under VMware Fusion 4, so have a look at: 
Change the Compatibility of a Virtual Machine
After changing the Hardware Compatibility uninstall VMware Tool, reboot and then once back at the Desktop shutdown, not suspend the Virtual Machine.
Open the Virtual Machine Package and delete the Applications and appListCache folders from within the Virtual Machine Package.
Uninstalling VMware Fusion 5.x and install VMware Fusion 4.x and then start the Virtual Machine and once at the Desktop install VMware Tools.