If I understand correctly you are putting down a laminate that is glued in place. That means hammer the staples flat or remove them, or a combination. If you really want to remove the staples try a pair of vice grips and roll them over a thin piece of battening to remove the staples. Depending on the type of staple and the wood they are in it may just rip the middle of the staple out and leave the rest.(If you have ever tried to remove the slats off a modern pallet you will know the problem)For the real piggy ones just zap them with an angle grinder
It will be a tedious job whichever way you go.
Another possibility is clunk click laminate with an underlay fibre layer that will absorb slight irregularities.