A heads up about typical "name" cherry trees propagated at nurseries. Cherry trees are almost always grafted on to special rootstock varieties. Rootstocks are selected to give grafted trees advantages in cold hardiness, disease resistance, fruit quality, and size control. Depending on your local climate, soil and prevalence of diseases, there will be rootstocks that are favored for your area.
If you air layer a branch of your tree and it is a typical grafted nursery tree, the resulting air layer will make the same type fruit as the parent, but it will likely be inferior in other performance aspects to the original tree. Apple trees, stone fruits, citrus are some of the varieties of fruit that there are very valuable advantages in going to the trouble of grafting to rootstocks. Fig trees are somewhat unique among fruit trees in not having big advantages in specialized rootstocks
I'm not trying to dissuade you from the project, it could be interesting and could result in a nice tree. There is the potential for the result to be a tree that far under performs its parent though. Just a heads up on a potential disappointment with the outcome years down the way.