Dried finger or palm prints will need longer soaking times, warmer water temperatures (within reason), or both. Added energy, in the form of mechanical scrubbing, is best applied using an ultrasonic cleaning bath. With ultrasonic cleaning, it can take seconds to dissolve dried finger/palm prints. Without it, hours.
No detergent is capable of damaging vinyl. This includes detergents with a caustic alkaline pH, such as electric dishwasher detergents or lab detergents like Alconox. They are aggressive enough to remove glued-on labels from records, they will seriously dry out the skin on your hands, but they cannot harm the vinyl.
Soaking records in alcohol can work, but it will not work better than detergents.
With any detergent, it is critically important to avoid using too much detergent, and after washing, to thoroughly rinse off all detergent. To start, use only very little concentrated detergent when you mix it with water. I use 1 or 2 drops of liquid dish washing detergent added to a gallon of water. If the water becomes visibly sudsy, you've added too much detergent.
After washing, rinse with water, two or three rinses. You must not let any detergent remain on the record's surface. It will only provide more opportunities for dust to stick.
After the final water rinse, I find it useful to spray on a 3 parts water/1 part alcohol mix. A simple plant sprayer works well for this. Use either ethanol or isopropanol. Alcohol mixtures sold as "denatured alcohol" are also OK for this. Water alone can bead up on a record's surface as it dries. The water/alcohol mix prevents beading and allows the record to dry faster. You don't need to spray on much volume to prevent water beads.