I don't raise turkeys, but I do raise grey and green jungle fowl, vulturine guinea fowl and several species of pheasants. I candle some of my eggs every other day until I can see good growth, from about day 3 until day 10 or so and again every so often until just before the hatch date. Candling doesn't hurt the eggs and if you are careful there should be no reason your hands hurt the eggs any more then turning the eggs every 4 hours if you don't use an automatic turner. Last year was the first time ever that I got 100% hatch rate, I raised birds as a child up until about 16 years old for 4-H and then took a long break, but even back then I have never had a perfect season. I am not an expert, and like I said I have not raised turkeys but I don't see a problem as long as you are careful with each egg.
If handling eggs is a problem I would be interested in why, if you let a hen sit on them she moves them around and touches them as well as leaves them for food and water throughout the entire incubation period, what is the difference between that and clean hands with gentle handling?