They'll be fine, I run cup dampers with eibach pro springs on my 172 but to be fair my old rear shocks were leaking fluid everywhere by the time I got round to changing them.
As for the actual process of swapping them over its pretty simple really just a bolt at the bottom and a nut on top. As long as you're relatively confident and have the tools to hand then it's not the hardest job to do (read below to see why I say make sure you have the tools to hand)
You'll need a jack and some axle stands too, simply jack up the rear and sit on stands then use the jack to hold the rear axle at the correct height as when you take the bottom bolt out the axle will pivot away and the springs will drop out.
The top nut may well be semi seized to the shock and will cause the piston to spin around, as mine were being replaced I clamped some mole grips onto the piston to stop it from spinning around allowing me to undo the top nut, obviously though this only works if you are replacing the shocks as they will get chewed up in the process and be unusable afterwards.
Installing is the opposite of above although I would personally wait until the car is back on its wheels before tightening the top nut up fully as the weight of the car will hekp to stop everything spinning around.