Is there a APFT wavier in order to put in a packet to attend WOCs?

Yes. There is a waiver available that you can submit with your packet. However, not many are approved. If your waiver isn't approved, you won't even make it to the board. Also, as WO1 Gerson mentioned, you are still required to complete all other running/rucking events in WOCS, so if you aren't able to run at all, that would pose a large problem.

There is a waiver.
I am not sure about the process, or what it gets into. I am a recent WOCS graduate from a class which had soldiers on permanent profile.

In my WOCS class we actually had two candidates that were on a permanent profile. One attended after being in almost the exact situation you are in. While you may do the 2.5 mile walk, you must be able to complete the other two events without issue. Also, this profile did not excuse them from the 10K, full load, ruck march. They had to complete everything that we did minus the running. The two candidates did complete all of the requirements and did graduate in my class.

For further information, both candidates were active duty soldiers, branched Intel and AG. I know at least one of them had to do some significant work with their branch to be able to attend.

Nope. Can't even be on profile.