I think the air influx (pending you have little head space) will be negligible. If you are trying to clear, how long has it been sitting and at what temperature? My ciders always clear, but some of them kick of lees up to a year. However, I would venture 85-90 percent of the lees are kicked off in the first 3-4 months of bulk aging.
My recc is, slowly lower the temperature to to around 45-55F and keep it stable. Leave it out of light, etc. and let it sit for minimum 2-3 months from start of fermentation. The cider will clear. Any air you take in will be minimal.
That said, you can leave the cider at around 60-65F and the cider will clear as well. Any tem right around 60F will work for aging or storage for a few months. Once it clears where you can read words on a sheet of paper through it, then you can bottle. Just keep in mind, if you don't give it a good bulk age, you will have extra lees in your bottles - not a big deal, just careful pours when you dig into them.
Some people use pectinase, I don't. You need to use that before fermentation though.