To some extent cartridges are self cleaning when inserted into a working printer and cycled. But you can do some manual cleanup to avoid soiling other printers. Work well after sunset outdoors (so there is no UV nor bright light) or someplace dim indoors but where you can make a mess then cleanup. You will need a supply of clean cotton balls (sterile is overkill).

First figure out which way the drum has to rotate with the paper movement. Clean the outside toner mess best you can with an old paint brush over newspaper, then flip open the drum shutter and secure it open with tape.

Using the cotton balls gently stroke the drum surface to pickup most of the toner. Discard each ball when the initial working side is dirty, do not reverse the ball and wipe fingerprint oil onto the drum. Rotate the drum using the gear on the end in the proper direction only to reveal more drum surface that may need wiping. Do not press hard (danger of scratching the drum), just try to dust most of the excess toner off. There is an internal squeegee system that will try to remove the rest over the next few print cycles.

Do not inadvertently get any breath moisture or cleaning fluids on the drum, which needs to have uniform highly insulating properties at the surface. If you wipe down the outside of the cartridge with anything damp, there could be tiny droplets that get past the shutter and spot the drum surface so be cautious.

The paper pickup cam thing is a pair of textured surface wide rubber bands stretched over flanged plastic cams. If you have enough rubber left, you can rotationally shift the rubber on the cam to put intact and unworn rubber over the highest points of the cam, the only part that matters. Some disassembly and reassembly will be required and you need to mark the original rotational alignment and get it put back right. If you can get new rubber, better still.