Be brave!

We prune the apple trees to take out dead wood, to let more light into the branches and to encourage the tree to put its strength into making a shapely tree and robust fruiting branches. 

You can remove up to 25% of the fruiting wood, the wood that bears buds, in any one year.  Leave it lying on the ground and you will see that it's quite a lot.  And dead wood doesn't count as part of your 25%, so you can take that out for free.

Take the branch right back to the trunk; you will see a wrinkle where the branch joins the trunk and you make the cut as close to that as possible on the branch side.  The tree will naturally scar over to seal the cut.

What you end up with is a tree with a root system that is working hard to put the energy into the places that you need it, the places where your best fruit will form.

Be brave!  Don't use secateurs except on very young trees.  Get in there with a saw and make the least cuts for the maximum effect.  

And when you have taken out your 25% walk away...no going back and fiddling!