There are rubber components in the cartridge assembly that could have dried out over 20 years. I remember they are part of the stylus suspension system, but I don't recall if they are located in the removable stylus piece or if they are located inside the cartridge body. Can you tell by looking at the stylus unit? Obviously, if they are part of the stylus unit, that's all I would replace.
Before you do that, consider that there may be other reasons why the sound quality seems to change with different LPs. For example, you may be aware that some LPs are significantly thicker now than LPs of old, and the difference in thickness results in a change in your vertical tracking angle (VTA). This in turn will affect the sound quality of the playback. You may be hearing that difference, or there may be something else. There might be nothing wrong with your stylus and cartridge. Good luck.