Depends on the cartridge/headshell interface, but one effective method that allows some micro-adjustment is to run a single, narrow (1-2mm) length of tape down the center of the cartridge. You can then tweak azimuth a little by altering the snugness of each mounting screw.
Different materials will have different effects on the sound, depending on how they interact with stray vibrations. This effect would be additional to/different from any sonic changes from azimuth.
Trial and listening is the only way to know what works best for you, as every system and every individual's sonic sensibilities are unique.