The Chilkat .NET assembly is a mixed-mode assembly, meaning that it exposes a managed API, but the inner core is native. Therefore, as for any DLL, a 32-bit process must load a 32-bit DLL, and a 64-bit process must load a 64-bit DLL.
On a 32-bit system, there is never any choice and therefore this whole subject is moot.
On a 64-bit system, a 100% managed .NET app can run as either a 64-bit process or as a 32-bit process. Visual Studio projects have a setting named "Prefer 32-bit", which is by-default ON, which means the app will always run as a 32-bit process. In that case, it is the 32-bit DLL that must be loaded (always), and again this subject is moot.
I recommend this: If your app does not use more than 4GB of memory, then simply choose to run 32-bit everywhere. You have better things to do with your time. Performance is usually just as good (if not better) running 32-bit.
I also recommend this: As time goes on, it gets more and more difficult to find yourself actually running on a 32-bit system. I'm sure it's been many years since it's been possible to buy a new computer running 32-bit Windows, and Microsoft is ending support for the OS's what can run 32-bit Windows. So.. if your app will NEVER encounter a 32-bit system, and it needs more than 4GB of memory, then uncheck the "Prefer 32-bit" setting in your Visual Studio app, and ALWAYS run 64-bit. Again, you have better things to do with your time than monkeying around with additional unnecessary complexity.
If you're in the situation where you desire either 32-bit or 64-bit, then there are two solutions: