First, consider fertilization. Non-cropping trees need nitrogen, but not as much as cropping trees. A general rule of thumb that has worked well in the past is to apply about half the normal rate of fertilizer. This will allow the trees to grow fairly normally without encouraging too much vigor. Some growers like to split their fertilizer application by applying half about a month before bloom and the second half around shuck split. The second half is applied only when the trees have a crop.
Trees with no crop also need to be pruned. Sometimes following a frost most of the fruit is in the tops of the trees and growers are reluctant to remove the crop. Due to frost in the south and low winter temperatures in the Midwest, the eastern peach crop will likely be short this year and peach prices should be good. So there will be an economic incentive to leave the trees a little higher than normal. This is an economic decision that each grower must make, but be aware that if branches are retained in the tops of the trees, it will take two or three years to bring tree height back to the original height.
For trees where no crop is expected, trees will benefit from a normal type of pruning.
Usually we try to keep the fruiting wood or "hangers" close to the scaffold limbs, so this would be a good time to remove secondary branches (branches that are 2 or 3 years old) arising from the scaffold branches. New hangers will develop along the scaffold branches this summer and the tree structure will be simplified.
There may be benefits to delaying pruning a few weeks later than normal. Early peach tree growth depends almost entirely on carbohydrate reserves from last season that are stored in the woody parts of the tree. If pruning is delayed until about 2 or 3 weeks after the normal bloom period, some of the growth that developed at the expense of those reserves will be removed and vegetative growth will be slightly suppressed this season.
Also consider summer pruning to retain fruiting wood in the lower part of the canopy.
Summer pruning about 2 to 3 weeks before harvest will slightly enhance fruit red color development with some varieties, but pruning in late June to early July is required to enhance flower bud formation and to keep hangers alive in the lower parts of the canopy. To retain fruiting wood in the lower canopy, consider pruning out vigorous upright shoots in late June.
Affects on Next Season's Crop
It's also important to realize that loss of this year's crop will affect next season's crop. Peaches are much less biennial than apples, but fruiting reduces the number of flower buds on the lower sections of the shoots that will be produced this summer. So there will be more flower buds per foot of shoot this winter, and you should plan to prune more aggressively next spring to lower the fruiting potential of the tree.
Also, trees with a light crop and trees that have been thinned during bloom have flower buds that are more tolerant of low winter temperatures. So winter survival of flower buds will be greater this winter for trees that did not crop this summer. The combination of higher flower bud density plus increased cold hardiness will likely lead to excessive crop loads next spring so be prepared to thin aggressively next spring.