but it wouldn't allow me to install a 32 bit version on my Window 7, 64 bit operating system.
Sorry but you can't install 32 bit version on 64 bit machine. Try instead 64 version.
You do not need to use the Admin Image tool when simply installing one copy of SolidWorks. Simply start the installation setup and select Individual installation, this should then install successfully on your machine.
You will require the 64 bit Install files for your machine as Deepak has said.