Eric R,
If you can post links to photos of the rivets and the tube-stem holes, people might be able to assess the condition/safety of your wheels.
If there is heavy rust around the rivets (especially if there is any looseness), you might not want to use the wheels.
I have used "rusty/rusted" wheels for many years on my Suburban. I blasted them and the rivets were tight; then, epoxy primed the bare metal; then, urethane finish coat. I have had no problems.
You might want to take your blasted wheels to a good/friendly tire shop to see if they can tell you that the wheels are true and can be balanced.