Unless you have experience with cherries I would advise against it but if you want to have a play give it a try. Keep in mind that cherry wood rots very easily and grafted trees are more difficult to layer.
Cherries are a pain. They get lots of diseases unless you know how to treat them properly and they die very easily.
They also need special pruning. They get disease easily if pruned at the wrong time. If you prune incorrectly they will not flower well.
Varieties that are grafted are often grafted because they are difficult to grow on their own roots so some of the varieties that we see as grafted trees are difficult to layer because they don't grow roots very well. If they do grow roots the roots may be weak and the tree will slowly die.
Having said all that what have you got to lose? If you have the time and space to try why not give it a go and see what happens?
Only thing I need to know.is best time to propagate, as you said wring time can stunt flowers which I have done a few times over the years on this tree.