This is a problem that currently cannot be solved, it's not just about 64-bit vs 32-bit, but the whole concept of loading binary libraries is simply not supported in the browser
In the future we might be able to support compiling such binary modules from C++ to Wasm, for the sake of loading them. But in the case of SWT they also depend on GTK (If I recall correctly) and hence X11. It would be an extremely large scale project.
One thing I'd like to add is that we could explore getting your specific use case to work, but it would be as part of a custom commercial project. Again, sales@leaningtech.com is the right point of contact if this seems interesting.
Not SWT in particular, any Java library that depends on binary components. Those binary components are compiled for a specific OS/Cpu, for example Windows on Intel