I've just been through this exercise.
Here's what I did and it was very successful.
Firstly, remove the slides from the cardboard mount and eventually remount using the GEPE plastic that you possess
This later action will most certainly benefit you when eventually scanning as using cardboard mounts can potentially leave fragments inside the scanner necessitating regular clean outs. They'll also keep the slide flatter and stiffer when scanning. Conversely, scanning unmounted with ANR glass holders will produce a sharper, larger and superior scan.
Now, the cleaning process.
First - get some lint free gloves to handle the slides - pointless leaving your greasy finger marks everywhere
Then use a hurricane type blower and remove all the small particles that may scratch your slide.
I then use the Invisible Dust sensor cleaning brushes that I have for my DSLR - this will lift any remaining particles. They don't damage my sensor so no fears on emulsion.
Then I use PEC12 solution and PEC-PAD lint free wipes
A few drops of the solution on the wipes and wipe across the slide (both sides) and bingo. Glistening clean slides.
I then polish them up a little using lint free clothes that I clean my camera lenses with. This ensures all potential smears are removed.
I've just finished a year long task cleaning and scanning some 2,00 very old, tarnished and pretty shabby slides/negatives and not one image was damaged using this process.
The recovery of images I thought long lost was amazing.
Hope this helps and as is customary I confirm I have no vested interest in the PEC products
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Great reply! Just the step-by-step procedure I was hoping to get.
Some minor follow-up items:
1 - When replacing the cardboard mounts with Gepe glassless mounts, where can I get computer-generated 35mm-size labels to indicate subject, source, exposure #, etc?
2 - Will any compressed air blowers work here or is a special brand for photographic purposes advisable? I have a Staples-brand "Dust Destroyer" that's "ozone safe - no CFCs." Can photo air blowers can ordered online?
3 - Can I order PEC12 solution and PEC-PAD lint free wipes online as well?