Word – How to set password on already existing winrar archive and encrypt it also

I solved this problem by converting the RAR archive to a TAR archive with IZArc, and then converting the TAR archive to an RAR archive with WinRAR (Tools-Convert-Compression for options). This preserved the date/time attributes, got past the problem that WinRAR won't convert a password protected archive (even though I know the password.)

Truecrypt is actually quite a good approach.

It has a "cache recently used passwords" option, so that if you mount your file, then un-mount it, the mount it again - it won't ask for the password the second time to save you time. You can (and by the sounds of things want to) turn this off, and which point it probably does what you want.