Thanks for the advice.
Mike, I don't suspect health problems, it's just that the larger lopsided stem has beaten the other to the light. The larger one is on the south side of the tree, which may explain.
Mario, the union does look strong, with a nice U shape rather than a V shape.
I'm pleased that noone thinks I'll be doing the wrong thing. The reason I posted the question was that I once did some formative pruning on a Norway maple standard (5 yrs old or so). One shoot, starting from half way up the tree, had gone out then turned parallel to the stem and raced ahead of the rest of the crown. I removed this at its point of origin. It didn't seem that drastic a move, but it must have upset the tree, as it produced a fair amount of epicormic growth, especially around the wound.
The same job involves reshaping an Acer platanoides 'crimson king'. Here, I'm planning to reduce a few branches on the south side, to balance a lopsided crown. The tree has probably been shaded on one side by a Robinia, but we are removing this one altogether, as the root plate has been lifted by the recent storm. Luckily, I don't need to touch the top, so I don't expect to see too much growth disruption if I take it easy. A light reduction this year, and maybe some follow up next year, depending on how the tree is doing taking over the space now occupied by the robinia. We'll be pulling out any crossing branches at the same time, whilst removing no more than 10% of the foliage - less if possible.
I'm really excited about doing this work because, for once, its a chance to do some formative pruning work which, in balance, should extend the life of the trees. These are all around 15 years old, have plenty of room to develop, and more importantly have a fairly clued up owner who's looking years ahead and is not whingeing about them being too high and dropping too many leaves. Most trees in this particular area are hacked at about the 15 foot mark. The neighbour has three giant hat racks which were silver birch trees. This is the sort of work I started out to do, but probably takes up 10% of my time..