The comparative costs of surplus military and commercial hunting ammo hardly make this a worthwhile exercise anymore. Besides, why use stale old re-cycled MILSURP ammo for hunting given the costs of everything else involved? Military hard point bullets with the tips opened up do not have predictable performance or accuracy for hunting, so this is not the way to go.
Some Milsurp ammo, notably US .30-06 ball, features an asphalt sealer inside the neck for waterproofing. These ones are a bear to pull, so you need to seat the bullet a bit further with a seater die to break this seal before pulling the bullet. You then need to clean the bullet off with solvent before re-seating it.
If you do this you must re-size the neck to establish proper bullet tension. As pointed out, remove the decapping pin to avoid detonating the primer in the process. Alternatively, you can use a Lee factory Crimp Die after seating the bullet. There will be enough tension left in the case neck after pulling to hold the re-seated bullet in place before crimping.
Re-cycling military 7.62 and .30-06 ball ammo by pulling the original bullet and replacing it with a match bullet of the same weight was once a common practice, known as "Mexican Match" ammo. If doing this with a different weight of bullet, the differential in bullet weight, as well as the unknown nature of the propellant, means that the powder should be discarded and replaced by a new charge of known propellant suitable for the heavier replacement bullet.
