You will not damage the stylus suspension by using a cleaning solution on your records that has alcohol. The cleaning solution is vacuumed off, and any minute residual amounts of alcohol on the record surface will evaporate in moments. (I have been using a homebrew record cleaning solution for 30 years that has alcohol, and have never noted any damage to the cantilever suspension.)
The advice to avoid using alcohol to clean the stylus tip itself, however, is probably sound. Any fluid can migrate up the stylus cantilever to the suspension, and alcohol probably will degrade the suspension over time.
To clean the stylus on my cartridge (a Grado Reference), I use a battery-operated cleaning device that was made some years ago by Signet, and may still be available. The device looks like a thick pen, and has a small circular patch of stiff bristle at the end. When you turn the device on, the bristle pad vibrates at about 400 Hz. You place the stylus tip on the bristle pad, and slowly pull the pad across the stylus tip (from back to front). I have found this vibrating, dry cleaning method works very well, although you must obviously be careful not to damage the cantilever.
The advice to avoid using alcohol to clean the stylus tip itself, however, is probably sound. Any fluid can migrate up the stylus cantilever to the suspension, and alcohol probably will degrade the suspension over time.
To clean the stylus on my cartridge (a Grado Reference), I use a battery-operated cleaning device that was made some years ago by Signet, and may still be available. The device looks like a thick pen, and has a small circular patch of stiff bristle at the end. When you turn the device on, the bristle pad vibrates at about 400 Hz. You place the stylus tip on the bristle pad, and slowly pull the pad across the stylus tip (from back to front). I have found this vibrating, dry cleaning method works very well, although you must obviously be careful not to damage the cantilever.