When I’m going to spin on a new-to-me wheel, I like to have a field kit of things I might need to adjust the wheel.

Cotton string is useful if the drive band is missing or needs to be replaced. It can also be used to tie up loose parts, or slow the spin on a bobbin (for a Lazy Kate). It is always a good idea to have some string.
The leather scrap is there for making parts. Most often I need a washer to improve the fit, especially on older wheels whose wooden parts have sagged. A heavy pair of scissors and a scrap of leather can make many, many things.
Beeswax is used on the drive band to give it some grip. The most important thing to do with an unfamiliar wheel is to check the alignment of the wheel with the whorl. Then check the tension. A little bit of wax along the string can then give more advantage. Beeswax is good for wood, so will cause no damage.
Oil is for the bearings and places friction occurs, like the connections of the flyer, or bobbin, or spindle. I used it sparingly, usually just one drop is enough.
The bamboo skewers or toothpicks can replace a missing post pin, or be used as a wedge. They were an unexpected bonus to have when I was working with a Great Wheel. I think I will add tissue paper to my next kit, as a bit of tissue paper around a post end can tighten up the fit.
A scrap of cloth for wiping away dust and old oil would be a good idea too.