Hiya

We had the same problem when we moved into our holding last year - the previous tenants had let the old cherry trees run a bit wild & there were loads of dead branches on them. We did trim them a fair bit & they did fruit last summer - though the birds got all the cherries

Trim to about a cm above a strong shoot at an angle so the rain drips away.
Apparently the "right" time to prune cherry trees is mid summer, when the new growth has matured, as they are known to "bleed". Use an antifungal paste on the site afterwards - they are known to be very sus to getting fungal infections, so you are supposed to clean your cutters in a weak bleach solution beforehand.
Hope you get some yummy cherries from them
