Health regeneration works as an init eventhandler script assigned to the Soldier:Man class in the main config so there are three ways to disable it.
1. Remove the heal.sqs script from Soldier:Man in the main config will disable all health regeneration.
2. Use addon units that inherit from Man rather than Soldier.
3. Use addon units that override the Eventhandlers class.
For options 2 and 3 this also means losing the swimming and secondary weapon scripts.
If you want to use addon units in an MWC mission then you'd need to manually add the swimming, secondary weapon and healing scripts to the unit when they spawn using the core game mode's SpawnDialog.sqs script or the wager match mode's respawn.sqs (in the same place they add mission specific fired and killed eventhandlers to the respawned unit). I guess I should put this information in the editor's guide but it's already 39 pages long!
EDIT: See release thread for download link.