Official US Navy word regarding specifically the OAR is, candidates have the option of doing paper or CAT for math, reading, and mechanical. Times for both versions are the same (40/30/15, respectively), no maximum number of questions for the CAT (which makes sense), the paper version has 30/20/30 questions, respectively. And I totally see the need for a joystick for the rest of the ASTB-E, but I'm only focused on the OAR portion. Thanks to all who helped me sort this issue.
I only proctor for active duty (as its a volunteer command collateral, I'm not a recruiter), and I specifically asked the APEX folks if the paper test was still an option, as I had quite a few people reach out to take it, but mentioned they would be deploying soon. I was told the paper copy was no longer an option.If you are AD you can have your ESO try to get a paper copy, but the NRD's were told specifically they are not to have any paper copies.
EDIT: This was ~ March 2021, so a few months ago.