Any 32-bit application should work fine on a 64-bit OS because of technology built into modern processors, and because of a “compatibility layer” built into 64-bit Windows. Believe it or not, you may run into more problems when trying to install 64-bit applications on a 64-bit OS because of dependencies. To put it succinctly, since not everything has been migrated to 64-bit yet (think of the sheer amount of code that would need to be rewritten to do that), a shared file that would be called by a new 64-bit app could still be living in 32-bit land. The new app might not like that so much and will force you to install the 32-bit version of itself on the computer to ensure that it plays nicely with all of the shared files. This might be the case with most applications related to ham radio since their development base is probably relatively small and they probably use a lot of shared code.
BTW, the only thing 64-bitness really gets you is the ability to address more physical memory. Unless you think your ham app is going to use northwards of 2GB of RAM all by itself, it’ll probably suffice to run 32-bit versions of everything, even on 64-bit Windows.
Drivers will probably be a bit pickier, although hardware vendors have been pretty good about developing both 32- and 64-bit versions of most drivers given the amount of time 64-bit Windows has been around now. It seems to me that most ham gear interfaces use pretty standard hardware that requires fairly generic drivers, so most of that will probably be worked out for you already. In other words, Cameron’s right