Borrow yourself a HeyWayne - a great contraption that is able to reach even the highest branches!
I pruned my apple tree last year after it only produced a handful of fruits. This year it is covered in tiny baby apples! To prune the top I used one of those extendable loppers - the ones with the hook at the end and a pull cord that moves the blade, hang on a minute (goes to google..)
Spear & Jackson Razorsharp Garden Telescopic Tree Pruner & Saw Max Length 2430mm - 4930FZ/03 - S/J4930FZ - Spear & Jackson Tree Pruners
This is actually the same as the one I have. The saw bit is a bit rubbish, but I've used the pull-blade bit to cut branches a couple of inches thick.
As for cutting the larger "stems" I think as long as you a) do it during the dormant period, b) cut cleanly with no "flat" surface and c) make sure you leave plenty of other growth on the tree, you should be okay.
I'm sure Monty cut a large branch off one of the apple trees at Berryfields last year as he kept banging his head on it...I know that feeling!