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.

The short answer is no.

Here is the guidance off of the USAREC page. It is waiverable and you should submit the waiver request and continue with your packet. The short answer is not NO, I hope this helps.

APFT WAIVER GUIDANCE: Per AR 350-1, paragraph 3-14a, Soldiers with medical profiles due to operational deployment will be permitted by their immediate commanders to attend appropriate courses (to include PME) within the guidelines of their profile. Soldiers must arrive at the aforementioned courses of instruction with a copy of their current profile and a memorandum signed by their commander stating the profile is a result of injuries sustained due to operational deployment. Per AR 350-1, paragraph 3-13j(3), Candidates applying to WOCS or OCS must pass the standard three-event APFT as a enrollment requirement. An exception to policy may be granted by HQDA DCS, G3/5/7 for a permanent profile to the running event only. The exception only allows the Soldier to apply to compete for entry into WOC or OCS school. The permanent profile must be a result of extraordinary circumstances.

Talk to a Warrant Officer recruiter.