Acer reshaping from a cube

When I moved into my house I inherited two acer trees.  The previous owners had been cutting them like a box hedge and they have been steadily growing as two massive cubes. I was wondering, if I were to go in and heavily prune them now (then stop attacking them with a hedge cutter), is there any way they will recover and go back to a more natural shape?  They seem to grow very quickly and are nearly overgrowing my garden path, so I will need to keep on top of them with regular pruning.  Something needs to be done with them though and it seems a shame to dig them up.