Can I reduce the height of my cherry tree without killing it?

[Waaii]

I have a morello(?) cherry tree in my back garden. It is about 25 feet tall and has a diameter main trunk of about 11/2 to 2 feet.

Aprox. 4-5 feet from the ground the main trunk divides into 6 thick branches. A few fruiting branches go out from these at around 6-8 feet, all the rest are high above.

There are 3 problems, all the fruit is produced too high to pick, the birds get all the fruit, the huge canopy makes the house dark and shades a considerable part of the garden.

I have other large fruit trees but the cherry blossom is beautiful and I have a nice circular seat around the trunk.

QUESTION
What I would like to do and need advice on, is to cut the centre 2 relatively unproductive branches out and reduce the remaining 4 to about 8 feet max retaining as many fruiting sub-branches as possible.

This would be well above any graft (if one exists) I believe, and make it all much more manageable. But would I kill the tree? and is it possible or likely that it would generate new fruiting growth from the cuts?