You would have a better chance to move the tree during dormant season when there are no leaves. Around 90% of hazelnut roots are in the top 3 ft of soil, so actually they are rather shallow-rooted. If you go for it during the growing season, I would expect the tree, if it survives, to be very stressed for the next couple of years, maybe longer. Stressed trees often attract pests and make it easier for diseases to move in.  Clearly, getting as many roots as possible will be important, the expanse of the roots will roughly correspond to the edges of the canopy, the drip line. Other things to consider are to mark the orientation of the tree in its current site and plant it in the same direction and to the same depth, you may want to mark where the soil line is on the trunk before you dig. Also paint the trunk with white latex paint to prevent sunburn after planting. Irrigate the transplanted tree but don't over do it. Hazelnuts need good drainage so make sure the planting site is well-drained.

Also note that hazelnuts are self-incompatible and are usually planted paired with compatible pollinizer trees to improve production.