Probably not a good idea. Pruning while they are in fruit may stress them and cause them to drop the fruit prematurely. They need to be pruned when they are dormant - that is, in the fall or winter once they have lost all their leaves. You would be much better accepting what you have now in terms of the fruit and pruning them in the fall.

I think you can "trim" them lightly, just to accommodate the net, but nothing

more. I've done this pluots and peaches, without losing fruit.

Actually, summer pruning of fruit trees is a well accepted practice :-) Many orchardists prune their trees in summer. Pruning at different times of the year produces a different reaction by the tree - winter pruning is done to develop proper structural qualities and encourage fruit production in the tree while summer pruning is typically done to control size.....exactly what you are attempting to do :-)

Fruit trees: Summer pruning versus winter pruning.

Yes, you may lose some fruit. It is almost inevitable with any summer pruning but not nearly as much as you might think, since much of what you will be removing is long, whippy growth that has not yet developed its fruit bearing qualities.

And if you are new to fruit trees, you should read up on thinning as well. This is an important task for a home fruit grower as it both maximizes fruit size as well as benefits the overall health of the tree.

Just an FYI but an overgrown or neglected tree of any type is never pruned back into shape in a single season but over a period of multiple years, typically 3-5, often in both summer and during the dormant period.

You must be in the southern hemisphere if you have apples and apricots in fruit in December :-))