My described scenario would not necessarily reuse a k value. It could possibly use one of thousands of k values that would appear "random" unless you produced and inspected thousands of transactions that you ultimately did not broadcast.
Or unless you read the code to see how the k values were being generated, as I said above.
There are additional things that could happen that could cause your private key to become compromised while you are transferring the private key from a paper wallet to your computer, and these things are not possible if your private key was stored on your hard drive.
Provided you are importing your paper wallet to an airgapped computer in the privacy of your own house, and you don't have a camera pointed at you while you are doing it or something equally stupid, what kind of things are you referring to that make a paper wallet more risky than an airgapped wallet?