The RHS publication. "Growing Fruit" was first published in 1980. Written by Harry Baker it is an excellent book, and has a clear and helpful section on exactly this topic. It is illustrated by drawings rather than photographs but is none the worse for that.
The good news seems to be that pruning cherry trees as a fan shape seems perfectly viable, although usually where growing against a wall and not out in the open.
There is too much for me to reproduce here, and it starts with a maiden tree so not exactly applicable to one that has already had some pruning. Key points though are always prune in spring. Pruning is fairly harsh cutting the maiden tree back to just two strong laterals tied at 35 degrees to the horizontal. Take out the central stem just above the uppermost lateral. Second spring shorten each leader to about 12 inches. By the third spring you should have perhaps 6 to 9 well spaced leaders. Cut these back to about 24 inches. By now the main shaping is over and in future years prune as an established tree.
Now an observation of my own. Cherry trees can be very vigorous and forty years ago dwarfing rootstocks were rare. So the book mentioned above was written from that perspective. Once in a permanent position, and well cared for, your tree should not remain "dinky," and sad for long. I would be inclined to get it planted over winter, and do nothing next spring. Give it a year to get well established and then get your pruning program going the following spring.
In the meantime see if you can discover which rootstock is being used, and try to pick up a second hand copy of the above book. It's a gem, even though it doesn't include some of the most modern varieties. I'd not part with my copy for a £1,000.
P.S. A £1,000 did I say? Well go on then!
