Studying genitalia is a very importation work of odonatological research, dragonfly and damselfly are difference in structure of genitalia. Steps below will let you know how I do my analyzing of structure of penis organ of a male specimen of Gomphidae (Anisoptera, dragonfly) without damaging the specimen.
Specimens in my collection
Release the dried male specimen from envelope (zip bag)
Fix the specimen on a small foam board with insect pins
Transfer the specimen into a box
Prepare the hot water (left) and a syringe
Puming the hot water to second abdomen segment area without making other part be wet (about 2 or 3 times, up to how hard/dried specimen is)
Check the specimen if the second abdomen segment area already wet and flexible enough to access the penis organ.
Transfer specimen to larger foam board and fix the body, wings and abdomen
Move the specimen to microscope
Under microscopic view, dig out the penis organ of the dragonfly then fix it in visible position with insect pins
Tranfer the specimen in fix position into a box with silica-gel
Cover the box and keep in dark area until the specimen to be hard.
Now your specimen are ready for take photo or drawing of detail structure of penis organ.
Some my completed figures of penis organ of Gomphidae for publication