I normally get a duster, flick a few drops of water on duster so it is slightly damp, then carefully, with circular movements, clean up the reels. Does the trick quite well and avoids solvents. All my bandits go through this treatment and the strips looking super. It's often bits of old grease or oil and wipes away nicely.
For really stubborn spots, I find the edge of a 1NP (or anything small without milled edge) carefully placed sideways, parallel to the spot on the reel, can help pick it away without tearing the strips, once again caution required.
Another method I have used for my other line of collectibles, vintage Star Wars action figures, is to use Servisol which was designed for switches, video head cleaning. I had six old carded figures where stickers had been removed from the card leaving sticky residue. When you spray a small amount of Servisol on to the card it breaks down the glue, almost freezes it so it falls away when rubbed with a slightly damp duster. The Servisol itself evaporates very quickly, therefore not leaving fluid everywhere. It's something you should be very cautious of doing. I've done quite a lot this way and they now look superb. Also good on plastics. Experiment on one symbol and see how it goes before building up confidence on others. For starters stick with the damp duster.
I'm sure everybody will have their way of doing things, think somebody suggested Mr Sheen polish once on here. Always a conundrum though, to leave as is and intact or have a go at making them better with the risk of causing some damage.