I recently "inherited" several rounds of .30-06 ammunition which I would like to safely dispose of.

The shoulders have light corrosion, as do the primers.

Should I be concerned regarding the stability of the primers before whacking the heck out of the rounds in an inertial puller.

Much prefer "field tested" advice over seat-of-the-pants guesses

An inertial bullet puller is specifically designed to unload a round safely, without detonating the primer. You should be fine.

That said, be careful with that old ammunition. Pull the bullets outside, wearing eye protection, and keep the business end of the puller away from your body. Then simply recycle the bullets, trash the cases, and pour the powder out in your garden, it'll help add nitrogen to the soil. (Decomposing nitro-cellulose)

One thing that will make this job easier is to run the old cartridges up into a seater die with it adjusted to seat the bullet slightly deeper into the case. This will break the bond between the case neck and the bullet, making it much easier to get the bullet out of the case.

+1 on what roberto said.