I'd think very carefully before taking a hacksaw to the bottom bracket shell. It needs to be cut accurately for length and also 100% straight or new bearings won't last very long. If you insist on doing this you don't necessarily need to pay a frame builder as any decent engineering shop should be able to do it. I like to do things myself where possible but this would be one job I'd definitely farm out to someone with the skills and tools to it accurately.
These things can be done but I don't see any point. The Raleigh chainwheel is a work of art, will outlast anything you can buy today and properly polished chrome chainsets look beautiful and properly installed cotterpins will work for thousands of miles. A lot of online "experts" say they don't work but they do in practice and people have cycled around the world on cottered chainsets. Proper installation is the key. They also will be easily removed if installed properly.
An R20 will always be a heavy bike no matter what you do and it is not a performance orientated machine so there is nothing to gain (IMO) from changing it to square taper.