Is it possible to stop Zerg regeneration? Like... if a Zerg unit gets hurt, for its HP to just stay at that value.

Short answer: no. You'd have to modify memory or use a virtual HP system.

I suppose you could hit it with a direct damage system in time to the regeneration rate to cancel out the regeneration...

The "traditional" solution is just to give everything such huge HP and damage amounts that the regeneration becomes effectively negligible, but I get the feeling that that might not be suitable for your purposes.

I'm using armor in such a way that I can't scale up attacks too much (up to 400 dmg, 140 armor).
It's turn based though so I could perhaps let units attack longer, allowing for large HP scaling.

Yeah, in that case, using DDS to cancel out the regeneration might be the way to go...especially since you can take liberties with the units in a turn-based game when they're not active in order to keep the scarab splash from affecting anything else.

All you've got to do is look up the number for the exact amount of regeneration per unit time, then periodically cycle through all the zerg units and harm them with the DDS just enough to remove the regenerated health. A slight increase to the maximum HP will keep unhurt zerg units from being weaker as a result of this system.

4/256 hp per frame, sc runs at 16 frames per game second, 8 hyper triggers per game second. The minimum damage you can do is 128/256 damage, so if you use a scarab after 16 trigger runs that should work.

Actually I think it'd be best if you wouldn't fight the regeneration but embrace it. StarCraft is as successful as it is because there's 3 different race but the damage mechanics are forged in a way that allows for pretty good balance through diversification.

What I'm saying is change your map concept/balance so some of your units have regeneration, but a slight disadvantage in another field. A map will always have a better feel if you try to adapt your it to the limits of sc rather than try to fight sc's limits to achieve your concept.