Okay, I use hand levers almost exclusively. The type of hand lever is important, and of course how you use them and protect the dial and hands is also important.
A reference photo:
The Speedmaster movement is in it's movement holder, the hands are set for removal, and although some are hidden there are 2 sets of hand levers there. In addition you will see several sets of plastic...
For removing the sub-dial hands, I use the smaller/narrower set of levers, and I first place the plastic bag you see there over the hand. The levers are carefully wedged under the sub-dial hands (over the bag), and levered up.
The central chronograph seconds hand is done next using the larger set of levers, and I raise the surface that I lever on with the thicker piece of plastic that has the slot cut in it. This is made of several layers of thick plastic that is used to wrap watches in - it's quite thick and adheres to itself via static cling. You could also use those static sling style crystal protectors for this - stack them and cut with an Exacto knife. I can add or peel layers off to get the correct height. It also protects the dial of course.
Once the central seconds hand is removed, I use the thinner piece of plastic with the slot cut in it, and the larger levers, and I remove the hour and minute hand together unless they are on really tight.
If you have the hands launch away (I tend not to have this - lever the hands off slowly) then you can cover the hand in question with a plastic bag and this will prevent the hand from flying away. I do this on the sub-dial hands, but not typically on larger hands. If you do this on larger hands, make sure the bag does not press down on the ends of the hands and bend the hand.
Of course the design and condition of your hand levers is critical. These are the best hand levers I have ever used, and I have used many brands. These are made by VOH - I know I am a walking advertisement for this company, but they make great tools IMO. You can see that the curve of the tip is very severe, so you get a lot of vertical movement of the tips with a small change in angle of the levers. So I don't have to pry much to get the hands off - it takes surprisingly little movement of the levers compared to levers that have a shallower angle between the tip and handles. Also, as with any tool that comes in contact with hands or dial, when I got these they were checked for burrs and polished, and they are checked for burrs before every single use. Trust me you don't want a burr on the bottom of your hand levers...been there, done that...not fun...
When levering off hands, you need to push inwards to grip on the OD of the hand's tube rather than just lever up under the rivet. This will help prevent tight hands, like on a chronograph, from coming apart while removing them. Still, sometimes no matter what you do the hand comes apart - more so on modern watches than vintage. Doing this will also grip the hand so it doesn't fly away when levering it off.
On a Speedmaster the hand that seems to fail more than any other is the minute recorder hand - it seems to be much tighter than the others for some reason when they are new.
Of course always go slow, think about what you are doing before you do it, and if you get frustrated or tired, walk away and leave it for another day.
Hope this helps.
Cheers, Al